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| {{Infobox scientist
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| | name = Gaetano Fichera
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| | image = Fichera.jpeg
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| | caption = Gaetano Fichera in 1976 (photo by Konrad Jacobs)
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| | birth_date = 8 February 1922
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| | birth_place = [[Acireale]]
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| | death_date = {{death date and age|1996|6|1|1922|2|8|df=yes}}
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| | death_place = [[Rome]]
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| | known_for = [[Linear elasticity]]<br>[[Mathematical analysis]]<br>[[Variational inequalities]]<br>[[Numerical analysis]]<br>[[Partial differential equations]]<br>[[Several complex variables]]<br>[[Signorini problem]]
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| | influenced =
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| | field = [[Mathematics]]
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| | prizes = [[Columbus Prize]] (1949)<br>[[Italian Minister of Education Prize]] (1961)<br>[[Antonio Feltrinelli Prize]] (1976)<br>Golden medal "[[Benemeriti della Scuola, della Cultura, dell'Arte]]" (1979)<br>[[Ivane Javakhishvili Medal]] (1982)<br>Medal of the [[University for Foreigners Perugia|University of Perugia for Foreigners]] (1993)
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| | nationality = Italian
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| | alma_mater = [[University of Rome La Sapienza|Università di Roma]], 1941
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| | doctoral_advisor = [[Mauro Picone]]
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| | doctoral_students = see the [[Gaetano Fichera#Teaching activity|teaching activity section]]
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| | work_institutions = [[Istituto Nazionale di Alta Matematica]]<br>[[Istituto Nazionale per le Applicazioni del Calcolo]]<br>[[Università di Trieste]]<br>[[University of Rome La Sapienza|Università di Roma "La Sapienza"]]
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| }}
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| '''Gaetano Fichera''' (8 February 1922 – 1 June 1996) was an Italian [[mathematician]], working in [[mathematical analysis]], [[linear elasticity]], [[partial differential equation]]s and [[several complex variables]]. He was born in [[Acireale]], and died in [[Rome]].
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| == Biography ==
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| He was born in [[Acireale]], a town near [[Catania]] in Sicily, the elder of the four sons of Giuseppe Fichera and Marianna Abate.<ref>The main reference about his personal life is the book {{Harv|Colautti Fichera|2007}}.</ref> His father Giuseppe was a professor of [[mathematics]] and influenced the young Gaetano starting his lifelong passion. In his young years he was a talented [[association football|football player]]. On 1 February 1943 he was in the [[Italian Army]] and during the [[Armistice between Italy and Allied armed forces|events of September 1943]] he was taken prisoner by the [[Nazist]] troops, kept imprisoned in [[Teramo]] and then sent to [[Verona]]: he succeeded in escaping from there and reached the Italian region of [[Emilia-Romagna]], spending with partisans the last year of war. After the war he was first in Rome and then in [[Trieste]], where he met '''Matelda Colautti''', which become his wife in 1952.
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| === Education and academic career ===
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| After graduating from the [[liceo classico]] in only two years, he entered the [[University of Catania]] at the age of 16, being there from 1937 to 1939 and studying under [[Pia Nalli]]. Then he went to the [[University of Rome La Sapienza|university of Rome]], where in 1941 he earned his [[laurea]] with [[Latin honors#Types|magna cum laude]] under the direction of [[Mauro Picone]], when he was only 19. He was immediately appointed by Picone as an assistant professor to his chair and as a researcher at the [[Istituto Nazionale per le Applicazioni del Calcolo]], becoming his pupil. After the war he went back to Rome working with [[Mauro Picone]]: in 1948 he became "Libero Docente" (free professor) of [[mathematical analysis]] and in 1949 he was appointed as full professor at the [[University of Trieste]]. As he remembers in {{Harv|Fichera|1991|p=14}}, in both cases one of the members of the judging commission was [[Renato Caccioppoli]], which become a close friend of him. From 1956 onward he was full professor at the [[Sapienza University of Rome|University of Rome]] in the chair of [[mathematical analysis]] and then at the [[Istituto Nazionale di Alta Matematica]] in the chair of higher analysis, succeeding to [[Luigi Fantappiè]]. He retired from university teaching in 1992,<ref>His last lesson of the course of higher analysis was published in {{Harv|Fichera|1995a}}.</ref> but was professionally very active until his death in 1996: particularly, as a member of the [[Accademia Nazionale dei Lincei]] and first director of the journal ''Rendiconti Lincei – Matematica e Applicazioni''<ref>This [[scientific journal]] is the follow-up of the older and glorious ''Atti dell'Accademia Nazionale dei Lincei – Classe di Scienze Fisiche, Matematiche, Naturali'', the official publication of the [[Accademia Nazionale dei Lincei]].</ref> he succeeded in reviving the reputation of this publication.<ref>See {{Harvtxt|Colautti Fichera|1997|p=14, footnote}}, and {{Harvtxt|Galletto|2007|p=142}}.</ref>
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| === Honours ===
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| He was member of several [[Academy|academies]], notably of the [[Accademia Nazionale dei Lincei]], the [[Accademia Nazionale delle Scienze detta dei XL]] and of the [[Russian Academy of Science]].
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| === Teachers ===
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| His lifelong friendship with his teacher [[Mauro Picone]] is remembered by him in several occasions. As recalled by {{Harvtxt|Colautti Fichera|2006|pp=13–14}}, his father Giuseppe was an assistant professor to the chair of Picone while he was teaching at the [[University of Catania]]: they become friends and their friendship lasted even when Giuseppe was forced to leave the academic career for economic reasons, being already the father of two sons, until Giuseppe's death. The young, in effect child, Gaetano, was kept by Picone in his arms. From 1939 to 1941 the young Fichera developed his research directly under the supervision of Picone: as he remembers, it was a time of intense work. But also, when he was back from the front in April 1945<ref>The episode is narrated in {{Harv|Colautti Fichera|2006|pp=30–31}}.</ref> he met Picone while he was in [[Rome|Roma]] in his way back to [[Sicily]], and his advisor was so happy to see him as a father can be seeing its living child. Another [[mathematician]] Fichera was influenced by and acknowledged as one of his teachers and inspirators was [[Pia Nalli]]: she was an outstanding [[mathematical analysis|analyst]], teaching for several years at the University of [[Catania]], being his teacher of [[mathematical analysis]] from 1937 to 1939. [[Antonio Signorini]] and [[Francesco Severi]] were two of Fichera's teachers of the Roman period: the first one introduced him and inspired his research in the field of [[linear elasticity]] while the second inspired his research in the field he taught him i.e. the [[Several complex variables|theory of analytic functions of several complex variables]]. Signorini had a strong long-time friendship with Picone: on a wall of the [[apartment building]] where they lived, in Via delle Tre Madonne, 18 in Rome, a memorial tablet which commemorates the two friends is placed, as {{Harvtxt|Fichera|1995b|p=47}} recalls. The two great mathematicians extended their friendship to the young Fichera, and as a consequence this led to the solution of the [[Signorini problem]] and the foundation of the theory of [[variational inequalities]]. Fichera's relations with Severi were not as friendly as with Signorini and Picone: nevertheless, Severi, which was one of the most influential Italian mathematicians of the first half of the 20th century, esteemed the young mathematician. During a course on the [[Several complex variables|theory of analytic functions of several complex variables]] taught at the [[Istituto Nazionale di Alta Matematica]] from the fall of 1956 and the beginning of the 1957, whose lectures were collected in the book {{Harv|Severi|1958}}, Severi posed the problem of generalizing his theorem on the [[Dirichlet problem]] for [[Several complex variables|holomorphic function of several variables]], as {{Harvtxt|Fichera|1957|p=707}} recalls: the result was the paper {{Harv|Fichera|1957}}, which is a masterpiece, although not generally acknowledged for various reasons described by {{Harvtxt|Range|2002|pp=6–11}}. Other scientists he had as teachers during the period 1939–1941 were [[Enrico Bompiani]], [[Leonida Tonelli]] and [[Giuseppe Armellini]]: he remembered them with great respect and admiration, even if he did not share all their opinions and ideas, as {{Harvtxt|Colautti Fichera|2006|p=16}} recalls.
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| === Friends ===
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| A complete list of Fichera's friends includes some of the best scientists and [[mathematician]]s of the 20th century: [[Olga Oleinik]], [[Olga Ladyzhenskaya]], [[Israel Gel'fand]], [[Ivan Petrovsky]], [[Vladimir Gilelevich Maz'ya|Vladimir Maz'ya]], [[Nikoloz Muskhelishvili]], [[Ilia Vekua]], [[Richard Courant]], [[Fritz John]], [[Kurt Friedrichs]], [[Peter Lax]], [[Louis Nirenberg]], [[Ronald Rivlin]], [[Hans Lewy]], [[Clifford Truesdell]], [[Edmund Hlawka]], [[Ian Sneddon]], [[Jean Leray]], [[Alexander Weinstein]], [[Alexander Ostrowski]], [[Renato Caccioppoli]], [[Solomon Mikhlin]], [[Paul M. Naghdi|Paul Naghdi]], [[Marston Morse]] were among his friends, scientific collaborators and correspondents, just to name a few. He built up such a network of contacts being invited several times to lecture on his research by various universities and research institutions, and also participating to several [[academic conference]]s, always upon invitation. This long series of scientific journeys started in 1951, when he went to the USA together with his master and friend [[Mauro Picone]] and [[Bruno de Finetti]] in order to examine the capabilities and characteristics of the first [[electronic computer]]s and purchase one for the [[Istituto Nazionale per le Applicazioni del Calcolo]]: the machine they advised to purchase was the first computer ever working in [[Italy]]. The most complete source about his friends and collaborators is the book {{Harv|Colautti Fichera|2006}} by his wife Matelda: in those reference it is also possible to find a fairly complete description of Gaetano Fichera's scientific journeys.
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| The close fiendship between [[Angelo Pescarini]] and Fichera has not his roots in their scientific interests: it is another war story. As {{Harvtxt|Oleinik|1997|p=12}} recalls, Gaetano, being escaped from [[Verona]] and hidden in a [[convent]] in [[Alfonsine]], tried to get in touch with the local group of partisans in order to help the people of that town who had been so helpful with him: they were informed about an assistant professor to the chair of higher analysis in Rome who was trying to reach them. Angelo, which was a student of mathematics at the [[University of Bologna]] under [[Gianfranco Cimmino]], a former pupil of [[Mauro Picone]], was charged of the task of testing the truth of Gaetano's assertions, examining him in mathematics: his question was:– "Mi sai dire una condizione sufficiente per scambiare un limite con un integrale (Can you give me a sufficient condition for interchanging limit and integration)?"–. Gaetano quickly answered:– "Non solo ti darò la condizione sufficiente, ma ti darò anche la condizione necessaria e pure per insiemi non limitati (I can give you not only a sufficient condition, but also a necessary condition, and not only for bounded domains, but also for unbounded domains)"–. In effect, Fichera proved such a theorem in the paper {{Harv|Fichera|1943}}, his latest paper written in while he was in Rome before joining the army: from that moment on he often used to joke saying that good mathematicians can always have a good application, even for saving one's life.
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| One of his best friends and appreciated scientific collaborator was [[Olga Arsenievna Oleinik]]: she cured the redaction of his last posthumous paper {{Harv|Fichera|1997}}, as {{Harvtxt|Colautti Fichera|2007|pp=202–204}} recalls. Also, she used to discuss his work with Gaetano, as he did with her: sometimes their discussion become lively, but nothing more, since they were extremely good friends and estimators of each one's work.
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| == Work ==
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| === Research activity ===
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| He is the author of more than 250 papers and 18 books (monographs and course notes): his work concerns mainly the fields of [[pure mathematics|pure]] and [[applied mathematics]] listed below. A common characteristic to all of his research is the use of the methods of [[functional analysis]] to prove [[existence theorem|existence]], [[uniqueness quantification|uniqueness]] and [[approximation theory|approximation theorems]] for the various problems he studied, and also a high consideration of the [[Mathematical analysis|analytic problems]] related to problems in [[applied mathematics]].
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| ====Mathematical theory of elasticity====
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| his work in [[elasticity theory]] includes the paper {{Harv|Fichera|1961c}}, where Fichera proves the "[[Fichera maximum principle]]", his work on [[variational inequality|variational inequalities]]. The work on this last topic started with the paper {{Harv|Fichera|1963}}, where he announced the existence and [[uniqueness quantification|uniqueness theorem]] for the [[Signorini problem]], and ended with the following one {{Harv|Fichera|1964a}},<ref>See also its English translation {{Harv|Fichera|1964b}}.</ref> where the full proof was published: those papers are the founding works of the field of variational inequalities, as remarked by Stuart Antman in {{Harv|Antman|1983|pp=282–284}}.<ref>These are his only papers in the field of [[Variational inequality|variational inequalities]]: see the article "[[Signorini problem]]" for a discussion of the reasons why he left this field of research.</ref> Concerning the [[Saint-Venant's principle]], he was able to prove it using a [[Calculus of variation|variational]] approach and a slight variation of a technique employed by [[Richard Toupin]] to study the same problem: in the paper {{Harv|Fichera|1979a}}<ref>The same paper was previously published in Russian in a volume in honour of [[Ilia Vekua]]: see {{Harvtxt|Colautti Fichera|1997|p=29}} for the exact reference.</ref> there is a complete proof of the principle under the [[hypothesis]] that the base of the [[Cylinder (geometry)|cylinder]] is a set with [[piecewise]] [[Smooth function|smooth]] [[Boundary (topology)|boundary]]. Also he is known for his researches in the theory of [[hereditary elasticity]]: the paper {{Harv|Fichera|1979b}} emphasizes the necessity of analyzing very well the [[constitutive equation]]s of materials with memory in order to introduce [[Scientific modelling|models]] where an existence '''and''' [[uniqueness quantification|uniqueness theorems]] can be proved in a such a way that the proof does not rely on an implicit choice of the [[topology]] of the [[function space]] where the problem is studied. At last, it is worth to mention that Clifford Truesdell invited him to write the contributions {{Harv|Fichera|1972a}} and {{Harv|Fichera|1972b}} for [[Siegfried Flügge]]'s ''Handbuch der Physik''.
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| ====Partial differential equations====
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| He was one of the pioneers in the development of the abstract approach through [[functional analysis]] in order to study general [[boundary value problem]]s for [[linear partial differential equation]]s proving in the paper {{Harv|Fichera|1955a}} a theorem similar in spirit to the [[Lax–Milgram theorem]]. He studied deeply the [[Mixed boundary condition|mixed boundary value problem]] i.e. a [[boundary value problem]] where the boundary has to satisfy a [[mixed boundary condition]]: in his first paper on the topic, {{Harv|Fichera|1949}}, he proves the first existence theorem for the mixed boundary problem for [[self-adjoint operator]]s of <math>n>2</math> [[Variable (mathematics)|variables]], while in the paper {{Harv|Fichera|1955a|pp=22–29}} he proves the same theorem dropping the hypothesis of [[self-adjoint operator|self-adjointness]]. He is, according to {{Harvtxt|Oleinik|1997}}, the founder of the theory of [[partial differential equation]]s of [[characteristics of PDE|non-positive characteristics]]: in the paper {{Harv|Fichera|1956}} he introduced the now called [[Fichera's function]], in order to identify [[subset]]s of the boundary of the [[Domain (mathematics)#Real and complex analysis|domain]] where the [[boundary value problem]] for such kind of equations is posed, where it is necessary or not to specify the [[Boundary value problem|boundary condition]]: another account of the theory can be found in the paper {{Harv|Fichera|1960}}, which is written in English and was later translated in Russian and [[Hungarian language|Hungarian]].<ref>See the bibliography {{Harv|Colautti Fichera|1997}}: some of the translated papers are available online from the [[All-Russian Mathematical Portal]].</ref>
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| ====Calculus of variation====
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| His contributions to the [[calculus of variation]] are mainly devoted to the proof of existence and [[uniqueness quantification|uniqueness theorems]] for [[maxima and minima]] of [[functional (mathematics)|functional]]s of particular form, in conjunction with his studies on [[variational inequalities]] and [[linear elasticity]] in theoretical and applied problems: in the paper {{Harv|Fichera|1964a}} a [[semicontinuity]] [[theorem]] for a functional introduced in the same paper is proved in order to solve the [[Signorini problem]], and this theorem was extended in {{Harv|Fichera|1964c}} to the case where the given [[functional (mathematics)|functional]] has general [[linear operator]]s as [[argument]]s, not necessarily [[partial differential operator]]s.
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| ====Functional analysis and eigenvalue theory====
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| It is difficult to single out his contributions to functional analysis since, as stated at the beginning of this section, the methods of functional analysis are ubiquitous in his research: however, it is worth to remember paper {{Harv|Fichera|1955a}}, where an important existence theorem is proved. His contributions in the field of eigenvalue theory began with the paper {{Harv|Fichera|1955b}}, where he formalizes a method developed by [[Mauro Picone]] for the approximation of eigenvalues of [[Operator (mathematics)|operator]]s subject only to the condition that their [[inverse function|inverse]] is [[compact operator|compact]]: however, as he admits in {{Harv|Fichera|1974a|pp=13–14}}, this method does not give any estimate on the approximation error on the value of the calculated (approximated) eigenvalues. He contributed also to the classical [[eigenvalue|eigenvalue problem]] for [[symmetric operator]]s, introducing the [[method of orthogonal invariants]].<ref>See {{Harv|Fichera|1974a|pp=33–127}}, {{Harv|Fichera|1978a}}, {{Harv|Weinberger|1999}} and references therein.</ref>
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| ====Approximation theory====
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| His work in this field is mainly related to the study of systems of [[Function (mathematics)|functions]], possibly being particular solutions of a given [[partial differential equation]] or system of such equations, in order to prove their [[complete set|completeness]] on the boundary of a given [[Domain (mathematics)#Real and complex analysis|domain]]. The interest of this research is obvious: given such a system of functions, every solution of a [[boundary value problem]] can be approximated by an [[infinite series]] or [[Fourier integral|Fourier type integral]] in the [[topology]] of a given [[function space]]. One of the most famous examples of this kind of theorem is [[Mergelyan's theorem]], which completely solves the problem in the class of [[holomorphic function]]s for a [[compact set]] in the [[complex plane]]. In his paper {{Harv|Fichera|1948}}, Fichera studies this problem for [[harmonic function]]s,<ref>See also the monograph {{Harv|Günther|1967}}.</ref> relaxing the [[Smooth function|smoothness requirements]] on the boundary in the already cited work {{Harv|Fichera|1955a}}: a survey on his and others' work in this area, including contributions of [[Mauro Picone]], [[Bernard Malgrange]], [[Felix Browder]] and a number of other mathematicians, is contained in the paper {{Harv|Fichera|1979c}}. Another branch of his studies on [[approximation theory]] is strictly tied to [[complex analysis|complex analysis in one variable]], and to the already cited [[Mergelyan's theorem]]: he studied the problem of approximating [[continuous function]]s on a [[compact set]] (and analytic on its [[Interior (topology)|interior]] if this is non void) of the [[complex plane]] by [[rational function]]s with prescribed [[Pole (complex analysis)|poles]], simple or not. The paper {{Harv|Fichera|1974b}} surveys the contribution to the solution of this and related problems by [[Sergey Mergelyan]], [[Lennart Carleson]], [[Gábor Szegő]] as well as others, including his own.
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| ====Potential theory====
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| His contributions to [[potential theory]] are very important. The results of his paper {{Harv|Fichera|1948}} occupy paragraph 24 of chapter II of the textbook {{Harv|Günther|1967|pp=108–117}}, as remarked by in {{Harvtxt|Oleinik|1997|p=11}}. Also, his researches {{Harv|Fichera|1975}} and {{Harv|Fichera|1976}} on the [[asymptotic analysis|asymptotic behaviour]] of the [[electric field]] near [[Smooth function|singular points]] of the conducting surface, widely known among the specialists (as several works of [[Vladimir Gilelevich Maz'ya|V.G. Maz'ya]], [[S.A. Nazarov]], [[B.A. Plamenevsky]], [[B.W. Schulze]] and others testify) can be included in between his works in potential theory.
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| ====Measure and integration theory====
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| His main contributions to those topics and are the papers {{Harv|Fichera|1943}} and {{Harv|Fichera|1954}}. In the first one he proves that a condition on a [[sequence]] of [[integrable function]]s previously introduced by [[Mauro Picone]] is both necessary and sufficient in order to assure that [[Limit (mathematics)|limit process]] and the [[integration (mathematics)|integration process]] commute, both in [[Bounded set|bounded and unbounded]] [[Domain (mathematics)#Real and complex analysis|domains]]: the theorem is similar in spirit to the [[dominated convergence theorem]], which however only states a sufficient condition. The second paper contains an extension of the [[Lebesgue's decomposition theorem]] to [[Sigma additivity#Additive (or finitely additive) set functions|finitely additive]] [[measure (mathematics)|measure]]s: this extension required him to generalize of the [[Radon–Nikodym derivative|Radon–Nykodim derivative]], requiring it to be a [[set function]] belonging to a given class and [[minimum|minimizing]] a particular [[Functional (mathematics)|functional]].
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| ====Complex analysis of functions of one and several variables====
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| He contributed to both the classical topic of [[complex analysis]] in one variable and the more recent one of [[Several complex variables|complex analysis in several variables]]. His contributions to complex analysis in one variable are essentially [[approximation theory|approximation results]], well described in the survey paper {{Harv|Fichera|1974b}}.<ref>See also the "[[Gaetano Fichera#Approximation theory|Approximation theory]]" section.</ref> In the field of functions of several complex variables variables, his contributions were outstanding,{{According to whom|date=April 2011}} but also not generally acknowledged.<ref>See the paper {{Harv|Range|2002}}.</ref> Precisely, in the paper {{Harv|Fichera|1957}} he solved the Dirichlet problem for [[Several complex variables|holomorphic function of several variables]] under the hypothesis that the [[Boundary (topology)|boundary]] of the [[Domain (mathematics)#Real and complex analysis|domain]] <math>\scriptstyle\partial\Omega</math> has a [[Hölder continuous]] [[normal vector]] (i.e. it is of <math>C^{1,\alpha}</math> class) and the [[Dirichlet boundary condition]] is a [[Function (mathematics)|function]] belonging to the [[Sobolev space]] <math>\scriptstyle H^{1/2}(\partial\Omega)</math> satisfying the [[weak formulation|weak form]] of the [[tangential Cauchy–Riemann condition]],<ref>Introduced by him in the same paper.</ref><ref>See also {{Harv|Fichera|1986}}, where the theorem is presented in English and extended to the case that the normal vector and the Dirichlet boundary condition are only [[Continuous function|continuous]].</ref> extending a previous result of [[Francesco Severi]]: this theorem and the [[Lewy–Kneser theorem]] on the [[Local property|local]] [[Cauchy problem]] for holomorphic functions of several variables, laid the foundations of the theory of [[CR-function]]s. Another important result is his proof in {{Harv|Fichera|1983}} of an extension of [[Morera theorem]] to [[Several complex variables|functions of several complex variables]], under the hypothesis that the given [[function (mathematics)|function]] <math>f</math> is only [[Locally integrable function|locally integrable]]: previous proofs under more restrictive assumptions were given by [[Francesco Severi]] in {{Harv|Severi|1931}} and [[Salomon Bochner]] in {{Harv|Bochner|1953}}. He also studied the properties of the [[real part]] and [[imaginary part]] of [[Several complex variables|functions of several complex variables]], i.e. [[pluriharmonic function]]s: starting from the paper {{Harv|Amoroso|1912}} he gives a [[Trace operator|trace condition]] analogous to the [[tangential Cauchy–Riemann condition]] for the solvability of the Dirichlet problem for [[pluriharmonic function]]s in the paper {{Harv|Fichera|1982a}}, and generalizes a theorem of [[Luigi Amoroso]] to the [[complex number|complex]] [[vector space]] <math>\scriptstyle \mathbb{C}^n\equiv\mathbb{R}^{2n}</math> for <math>\scriptstyle n\geq 2</math> [[Several complex variables|complex variables]] in the paper {{Harv|Fichera|1982b}}. Also he was able to prove that an [[integro-differential equation]] defined on the boundary of a [[smooth function|smooth]] [[Domain (mathematics)#Real and complex analysis|domain]] by Luigi Amoroso in his cited paper, the [[Amoroso integro-differential equation]], is a necessary and sufficient condition for the solvability of the Dirichlet problem for [[pluriharmonic function]]s when this domain is the [[sphere]] in <math>\scriptstyle \mathbb{C}^2\equiv\mathbb{R}^4</math>: details can be found in the paper {{Harv|Fichera|1982c}}.
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| ====Exterior differential forms====
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| His contributions to the theory of [[exterior differential form]]s started as a war story:<ref>He tells this story in his last lesson {{Harv|Fichera|1995a|pp=18–19}}: see also {{Harv|Colautti Fichera|2006|p=21}}.</ref> having read a famous memoir of [[Enrico Betti]] (where [[Betti number]]s were introduced) just before joining the army, he used this knowledge in order to develop a theory of [[exterior differential form]]s while he was kept prisoner in [[Teramo]] jail.<ref>This fact is not uncommon in talented people being kept in captivity, as the known experience of [[Jean Leray]] with [[sheaf theory]] shows.</ref> When he was back in Rome in 1945, he discussed his discovery with [[Enzo Martinelli]], who very tactfully informed him that the idea was already developed by mathematicians [[Élie Cartan]] and [[Georges de Rham]]. However, he continued work on this theory, contributing with several papers, and also advised all of his students to study it, despite from the fact of being an [[Mathematical analysis|analyst]], as he remarks: his main results are collected in the papers {{Harv|Fichera|1961a}} and {{Harv|Fichera|1961b}}. In the first one he introduced ''k''-measures, a concept less general than [[Current (mathematics)|currents]] but easier to work with: his aim was to clarify the [[Mathematical analysis|analytic structure]] of currents and to prove all relevant results of the theory i.e. the [[De Rham cohomology|three theorems of de Rham]] and [[Hodge theory|Hodge theorem on harmonic forms]] in a simpler, more analytic way. In the second one he developed an abstract [[Hodge theory]], following the [[axiomatic method]], proving an abstract form of Hodge theorem.
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| ====Numerical analysis====
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| As noted in the "[[Gaetano Fichera#Functional analysis and eigenvalue theory|Functional analysis and eigenvalue theory]]" section, his main ''direct'' contribution to the field of [[numerical analysis]] is the introduction of the [[method of orthogonal invariants]] for the calculus of [[eigenvalues]] of [[symmetric operator]]s: however, as already remarked, it is hard to find something in his works which is not related to applications. His works on [[partial differential equation]]s and [[linear elasticity]] have always a constructive aim: for example, the results of paper {{Harv|Fichera|1975}}, which deals with the [[asymptotic analysis]] of the [[Potential theory|potential]], were included in the book {{Harv|Fichera|1978a}} and led to the definition of the [[Hp-FEM#Example: the Fichera problem|Fichera corner problem]] as a standard [[Benchmark (computing)|benchmark problem]] for [[numerical method]]s.<ref>See also the recollections of Wendland in {{Harv|Wendland|2007|p=8}}.</ref> Another example of his work on quantitative problems is the interdisciplinary study {{Harv|Fichera|Sneider|Wyman|1977}}, surveyed in {{Harv|Fichera|1978b}}, where methods of [[mathematical analysis]] and [[numerical analysis]] are applied to a problem posed by [[biological sciences]].<ref>See also the research announcement {{Harv|Fichera|Sneider|Wyman|1977a}},</ref><ref>Note that {{harvtxt|Oeinik|1993|pp=12–13}} describes it as a work in the theory of [[ordinary differential equation]]s, perhaps reflecting the difficulty of classifying such kind of research.</ref>
| |
| | |
| ====History of mathematics====
| |
| his work in this field occupy all the volume {{Harv|Fichera|2002}}. He wrote bibliographical sketches for a number of mathematicians, both teachers, friends and collaborators, including [[Mauro Picone]], [[Luigi Fantappiè]], [[Pia Nalli]], [[Maria Adelaide Sneider]], [[Renato Caccioppoli]], [[Solomon Mikhlin]], [[Francesco Tricomi]], [[Alexander Weinstein]], [[Aldo Ghizzetti]]. His [[History of mathematics|historical]] works contain several observations against the so-called '''historical revisitation''': the meaning of this concept is clearly stated in the paper {{Harv|Fichera|1996}}. He identifies with the word '''revisitation''' the analysis of historical facts basing only on modern conceptions and points of view: this kind of analysis differs from the "true" historical one since it is heavily affected by the historian's point of view. The historian applying this kind of methodology to [[history of mathematics]], and more generally to the [[history of science]], emphasizes the sources that have led a field to its modern shape, neglecting the efforts of the pioneers.
| |
| | |
| === Teaching activity ===
| |
| His teaching activity was almost as intense as his research activity: he also was a pioneer in encouraging gifted women to choose a career in mathematical research, as {{Harvtxt|Weinberger|1999|p=51}} recalls. An almost complete list of his doctoral students is reported below:
| |
| <div style="-moz-column-count:4; column-count:4;">
| |
| *[[Lucilla Bassotti]]
| |
| *[[Caterina Cassisa]]
| |
| *[[Pieranita Castellani Rizzonelli]]
| |
| *[[Alberto Cialdea]]
| |
| *[[Maria Pia Colautti]]
| |
| *[[Luciano De Vito]]
| |
| *[[Flavia Lanzara]]
| |
| *[[Umberto Mosco]]
| |
| *[[Paolo Emilio Ricci]]
| |
| *[[Mirella Schaerf]]
| |
| *[[Maria Adelaide Sneider]]
| |
| *[[Giuseppe Tomassini]]
| |
| </div>
| |
| | |
| == Selected publications ==
| |
| All the works of Gaetano Fichera listed in this section, except {{Harv|Fichera|1964a}}, {{Harv|Fichera|1974a}} and also its [[translation]] {{Harv|Fichera|1978a}}, can be found in his "opere scelte" {{Harv|Fichera|2004}} or in the volume {{Harv|Fichera|2002}}.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Intorno al passaggio al limite sotto il segno d'integrale
| |
| | language = Italian
| |
| | journal = [[Portugaliae Mathematica]]
| |
| | volume = 4
| |
| | issue = 1
| |
| | pages = 1–20
| |
| | year = 1943
| |
| | url = http://purl.pt/2124
| |
| | mr = 0009192
| |
| | zbl = 0063.01364
| |
| }}. In "''On the passage to the limit under the sign of integral''" (English translation of title), a necessary and sufficient condition for the exchange of the [[limit (mathematics)|limit]] and the [[integral|integration]] [[operation (mathematics)|operations]] for [[sequence]]s of [[Integrable function|functions]] is proven, in the spirit of [[Henri Lebesgue]]'s [[Dominated convergence theorem]] (which, however states only a sufficient condition).
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Teoremi di completezza sulla frontiera di un dominio per taluni sistemi di funzioni
| |
| | language = Italian
| |
| | journal = [[Annali di Matematica Pura e Applicata]]
| |
| | series = Serie IV
| |
| | volume = 27
| |
| | issue = 1–2
| |
| | pages = 1–28
| |
| | year = 1948
| |
| | doi = 10.1007/BF02415556
| |
| | mr = 0029014
| |
| | zbl = 0035.34801
| |
| }}. "''Completeness theorems on the boundary of a domain for certain systems of functions''" is a classical paper in [[potential theory]].
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Analisi esistenziale per le soluzioni dei problemi al contorno misti, relativi all'equazione e ai sistemi di equazioni del secondo ordine di tipo ellittico, autoaggiunti
| |
| | language = Italian
| |
| | journal = [[Annali della Scuola Normale Superiore]]
| |
| | series = Serie III
| |
| | volume = 1 (1947))
| |
| | issue = 1–4
| |
| | pages = 75–100
| |
| | year = 1949
| |
| | url = http://www.numdam.org/numdam-bin/fitem?id=ASNSP_1949_3_1_1-4_75_0
| |
| | mr =0035370
| |
| | zbl = 0035.18603
| |
| }}. The paper "''Existential analysis of the solutions of mixed boundary value problems, related to second order elliptic equation and systems of equations, selfadjoint''" contains the first proofs of [[Existence theorem|existence]] and [[Uniqueness quantification|uniqueness theorems]] for the [[Mixed boundary condition|mixed boundary value problem]] for fairly general [[Domain (mathematics)#Real and complex analysis|domains]].
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Sulla derivazione delle funzioni additive d'insieme
| |
| | language = Italian
| |
| | journal = [[Rendiconti del Seminario Matematico della Università di Padova]]
| |
| | volume = 23
| |
| | pages = 366–397
| |
| | year = 1954
| |
| | url = http://www.numdam.org/item?id=RSMUP_1954__23__366_0
| |
| | mr = 0064858
| |
| | zbl = 0058.28302
| |
| }}. The paper "''On the differentiation of additive set functions''" is an important contribution to measure theory where the [[Radon–Nikodym theorem]] is extended in order to include [[singular measure|singular]] [[Finitely additive#Additive (or finitely additive) set functions|finitely additive measures]].
| |
| *{{Citation
| |
| | first = Gaetano
| |
| | last = Fichera
| |
| | editor-last = Fichera
| |
| | editor-first = G.
| |
| | contribution = Alcuni recenti sviluppi della teoria dei problemi al contorno per le equazioni alle derivate parziali lineari
| |
| | language = Italian
| |
| | title = Convegno Internazionale sulle Equazioni Lineari alle Derivate Parziali – [[Trieste]] 25–28 Agosto 1954
| |
| | year = 1955a
| |
| | pages = 174–227
| |
| | place = Roma
| |
| | publisher = Edizioni Cremonese
| |
| | mr = 0074665
| |
| | zbl = 0068.31101
| |
| }}. The paper ''Some recent developments of the theory of boundary value problems for linear partial differential equations'' details Fichera's approach to a general theory of [[boundary value problem]]s for [[linear partial differential equation]]s through a theorem similar in spirit to the [[Lax–Milgram theorem]]: as an application, the general existence and [[Uniqueness quantification|uniqueness theorems]] of previous paper {{Harv|Fichera|1949}} are proved dropping the hypothesis of [[self-adjoint operator|self-adjointness]] of the [[linear]] [[partial differential operator]]s considered.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Su un metodo del Picone per il calcolo degli autovalori e delle autosoluzioni
| |
| | language = Italian
| |
| | journal = [[Annali di Matematica Pura e Applicata]]
| |
| | series = 4
| |
| | volume = 40
| |
| | issue = 1
| |
| | pages = 239–259
| |
| | year = 1955b
| |
| | doi = 10.1007/BF02416536
| |
| | mr = 0075569
| |
| | zbl = 0065.35501
| |
| }}. English translation of the title:-"''On a method of Picone for the calculus of eigenvalues and eigensolutions''".
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Sulle equazioni differenziali lineari ellittico-paraboliche del secondo ordine
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Memorie. Classe di Scienze Fisiche, Matematiche e Naturali]]
| |
| | language = Italian
| |
| | series = Serie VIII
| |
| | volume = 5
| |
| | issue = 1
| |
| | pages = 1–30
| |
| | year = 1956
| |
| | mr = 0089348
| |
| | zbl = 0075.28102
| |
| }}. ''On linear elliptic-parabolic equations of second order''(English translation of the title) is the first paper on the theory of [[partial differential equation]]s of [[characteristics of PDE|non positive characteristics]]: the [[Fichera's function]] is introduced and its applications to the [[boundary value problem]]s for this [[Class (mathematics)|class]] of [[Operator (mathematics)|operator]]s is detailed. Also the [[Well-posed problem|well posedness]] is considered.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Caratterizzazione della traccia, sulla frontiera di un campo, di una funzione analitica di più variabili complesse
| |
| | language = Italian
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali]]
| |
| | series = VIII
| |
| | volume = 22
| |
| | issue = 6
| |
| | pages = 706–715
| |
| | year = 1957
| |
| | mr = 0093597
| |
| | zbl = 0106.05202
| |
| }}. "''Characterization of the trace, on the boundary of a domain, of an analytic function of several complex variables''" (English translation of the title) is an epoch-making paper in the theory of [[CR-function]]s, where the Dirichlet problem for [[Several complex variables|analytic functions of several complex variables]] is solved for general data.
| |
| *{{Citation
| |
| | first = Gaetano
| |
| | last = Fichera
| |
| | contribution = Spazi lineari di {{math|''k''}}–misure e di forme differenziali
| |
| | title = Proceedings of the Symposium on Linear Spaces, Jerusalem, 1960
| |
| | language = Italian
| |
| | year = 1961a
| |
| | pages = 175–226
| |
| | place = Jerusalem / Oxford
| |
| | publisher = Jerusalem Academic Press / [[Pergamon Press]]
| |
| | mr = 0133434
| |
| | zbl = 0126.17801
| |
| }}. "''Linear spaces of {{math|k}}–measures and differential forms''" (English translation of the title) is perhaps the most important contribution of Gaetano Fichera to the theory of [[exterior differential form]]s: he introduces the {{math|''k''}}–measures and shows that, despite being less general than [[Current (mathematics)|currents]] and thus being easier to work with, they can be used to prove all the most important results of the theory.
| |
| *{{Citation
| |
| | first = Gaetano
| |
| | last = Fichera
| |
| | editor-last = Langer
| |
| | editor-first = Rudolph E.
| |
| | contribution = On a unified theory of boundary value problems for elliptic-parabolic equations of second order
| |
| | title = Boundary Problems in Differential Equations
| |
| | year = 1960
| |
| | pages = 97–120
| |
| | place = [[Madison, Wisconsin|Madison]]
| |
| | publisher = [[The University of Wisconsin Press]]
| |
| | mr = 0111931
| |
| | zbl = 0122.33504
| |
| }}. A paper about the [[boundary value problem]] for [[partial differential equation]]s of [[characteristics of PDE|non positive characteristics]], where the [[Fichera's function]] is introduced and its application are described.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Teoria assiomatica delle forme armoniche
| |
| | journal = [[Rendiconti di Matematica e delle sue applicazioni]]
| |
| | language = Italian
| |
| | series = 5
| |
| | volume = 20
| |
| | pages = 147–171
| |
| | year = 1961b
| |
| | mr = 0140124
| |
| | zbl = 0116.07601
| |
| }}. "''Axiomatic theory of harmonic forms''" (English translation of the title) is a work containing an abstract theory [[harmonic form]]s in [[Hilbert space]]s, including a proof of [[Hodge theory#Hodge theory of elliptic complexes|Hodge theorem]].
| |
| * {{citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Il teorema del massimo modulo per l'equazione dell'elastostatica tridimensionale
| |
| | language = Italian
| |
| | journal = [[Archive for Rational Mechanics and Analysis]]
| |
| | volume = 7
| |
| | issue = 5
| |
| | year = 1961c
| |
| | pages = 373–387
| |
| | doi = 10.1007/BF00250770
| |
| | zbl = 0100.30801
| |
| | bibcode = 1961ArRMA...7..373F
| |
| }}. "''The maximum modulus theorem for the three-dimensional elastostatic equation''" (English translation of the title) is the article where the now called "Fichera maximum principle" is proved.
| |
| *{{citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Sul problema elastostatico di Signorini con ambigue condizioni al contorno
| |
| | language = Italian
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali]]
| |
| | volume = 34
| |
| | series = Serie VIII,
| |
| | issue = 2
| |
| | year = 1963
| |
| | pages = 138–142
| |
| | zbl = 0128.18305
| |
| }}. "''On the elastostatic problem of Signorini with ambiguous boundary conditions''" is a research announcement describing briefly Gaetano Fichera's solution to the [[Signorini problem]].
| |
| *{{citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Problemi elastostatici con vincoli unilaterali: il problema di Signorini con ambigue condizioni al contorno
| |
| | language = Italian
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Memorie. Classe di Scienze Fisiche, Matematiche e Naturali]]
| |
| | volume = 7
| |
| | series = Serie VIII,
| |
| | issue = 2
| |
| | year = 1964a
| |
| | pages = 91–140
| |
| | zbl = 0146.21204
| |
| }}. An ample memoir containing the detailed proofs of existence and [[Uniqueness quantification|uniqueness theorem]] for the [[Signorini problem]], translated in the English language as {{citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | contribution = Elastostatic problems with unilateral constraints: the Signorini problem with ambiguous boundary conditions
| |
| | title = Seminari dell'istituto Nazionale di Alta Matematica 1962–1963
| |
| | year = 1964b
| |
| | publisher = Edizioni Cremonese
| |
| | place = Rome
| |
| | pages = 613–679
| |
| }}.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Semicontinuity of multiple integrals in ordinary form
| |
| | journal = [[Archive for Rational Mechanics and Analysis]]
| |
| | volume = 17
| |
| | issue = 5
| |
| | pages = 339–352
| |
| | year = 1964c
| |
| | doi = 10.1007/BF00250470
| |
| | zbl = 0128.10003
| |
| | bibcode=1964ArRMA..17..339F
| |
| }}. In this paper Gaetano Fichera proves a [[semicontinuity]] [[theorem]] for [[functional (mathematics)|functional]]s depending on a general [[linear operator]], not necessarily being a [[partial differential operator]].
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | contribution = Existence theorems in elasticity
| |
| | year = 1972a
| |
| | title = Festkörpermechanik/Mechanics of Solids
| |
| | editor-last = Flügge
| |
| | editor-first = Siegfried
| |
| | editor-link = Siegfried Flügge
| |
| | editor2-last = Truesdell
| |
| | editor2-first = Clifford A.
| |
| | editor2-link = Clifford Truesdell
| |
| | series = Handbuch der Physik (Encyclopedia of Physics)
| |
| | volume = VIa/2
| |
| | pages = 347–389
| |
| | place = Berlin–[[Heidelberg]]–New York
| |
| | publisher=[[Springer-Verlag]]
| |
| | zbl = 0277.73001
| |
| | isbn = 3-540-13161-2
| |
| }}, ISBN 0-387-13161-2. The encyclopedic entry written by Fichera on existence problems in linear elasticity for the ''Handbuch der Physik'' on invitation by [[Clifford Truesdell]].
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | contribution = Boundary value problems of elasticity with unilateral constraints
| |
| | year = 1972b
| |
| | title = Festkörpermechanik/Mechanics of Solids
| |
| | editor-last = Flügge
| |
| | editor-first = Siegfried
| |
| | editor-link = Siegfried Flügge
| |
| | editor2-last = Truesdell
| |
| | editor2-first = Clifford A.
| |
| | editor2-link = Clifford Truesdell
| |
| | series = Handbuch der Physik (Encyclopedia of Physics)
| |
| | volume = VIa/2
| |
| | edition = paperback 1984
| |
| | pages = 391–424
| |
| | place = Berlin–[[Heidelberg]]–New York
| |
| | publisher = [[Springer-Verlag]]
| |
| | zbl = 0277.73001
| |
| | isbn = 3-540-13161-2
| |
| }}, ISBN 0-387-13161-2. The encyclopedic entry written by Fichera on problems with unilateral constraints (the class of [[boundary value problem]]s the Signorini problem belongs to) for the ''Handbuch der Physik'' on invitation by [[Clifford Truesdell]].
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Metodi e risultati concernenti l'analisi numerica e quantitativa
| |
| | language = Italian
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Memorie. Classe di Scienze Fisiche, Matematiche e Naturali]]
| |
| | series = Serie VIII,
| |
| | volume = 12
| |
| | issue = 1
| |
| | pages = 1–202
| |
| | year = 1974a
| |
| | mr = 0639162
| |
| | zbl = 0334.65002
| |
| }}. "''Methods and results concerning numerical and quantitative analysis''" is an extensive [[Survey article|survey]] on some results of [[numerical analysis]] (especially on numerical calculation of [[eigenvalues]]) and associated results of [[mathematical analysis]] obtained by Gaetano Fichera and his school: its updated English [[translation]] is the book {{Harv|Fichera|1978a}}.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = On the approximation of analytic functions by rational functions
| |
| | journal = Journal of Mathematical and Physical Science
| |
| | place = [[Madras]]
| |
| | volume = 8
| |
| | issue = 1
| |
| | pages = 7–19
| |
| | year = 1974b
| |
| | zbl = 0294.30034
| |
| }}. A survey paper about the theory of approximation of and by [[complex analysis|analytic functions of a complex variable]].
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Comportamento asintotico del campo elettrico e della densità elettrica in prossimità dei punti singolari della superficie conduttore
| |
| | language = Italian
| |
| | journal = [[Rendiconti del Seminario Matematico dell'Università e Politecnico di Torino]]
| |
| | volume = 32 (1973–74)
| |
| | pages = 111–143
| |
| | year = 1975
| |
| | url =
| |
| | zbl = 0318.35007
| |
| }}. ''Asymptotic behavior of the electric field and density of the electric charge in the neighborhood of singular points of a conducting surface'' (English translation of the title) is an important paper on the [[asymptotic analysis]] of the [[electric field]] near the [[vertex (geometry)|vertex]] of a [[cone (geometry)|conical]] [[Conductor (electricity)|conducting]] [[surface]]. There exists also a freely consultable Russian translation, {{Citation
| |
| | title = Асимптотическое поведение электрического поля и плотности электрического заряда в окрестности сингулярных точек проводящей поверхности
| |
| | language = Russian
| |
| | journal = [[Uspekhi Matematicheskikh Nauk]]
| |
| | volume = 30
| |
| | issue = 3(183)
| |
| | pages = 105–124
| |
| | year = 1975
| |
| | url = http://mi.mathnet.ru/eng/umn/v30/i3/p105
| |
| | mr = 388978
| |
| | zbl = 0318.35007
| |
| }}.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Asymptotic behaviour of the electric field near the singular points of the conductor surface
| |
| | journal = Rendiconti della [[Accademia Nazionale dei Lincei]], Classe di Scienze Fisiche, Matematiche e Naturali
| |
| | series = 8
| |
| | volume = 60
| |
| | issue = 1
| |
| | pages = 13–20
| |
| | year = 1976
| |
| | url =
| |
| | zbl = 0364.35004
| |
| }}.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | author-link =
| |
| | last2 = Sneider
| |
| | first2 = Maria A.
| |
| | author2-link = Maria Adelaide Sneider
| |
| | last3 = Wyman
| |
| | first3 = Jeffreys
| |
| | author3-link = Jeffries Wyman (biologist)
| |
| | title = On the existence of a steady state in a biological system
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Memorie. Classe di Scienze Fisiche, Matematiche e Naturali]]
| |
| | series = Serie VII, Sezione III
| |
| | volume = XIV
| |
| | issue = 1
| |
| | pages = 1–26
| |
| | year = 1977
| |
| | zbl = 0414.92004
| |
| }}. A work presenting a complete interdisciplinary analysis of the stability of a system of [[ordinary differential equation]]s containing a large number of parameters, modeling a biological system: the results presented here were later surveyed in the paper {{Harv|Fichera|1978b}}.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | last2 = Sneider
| |
| | first2 = Maria Adelaide
| |
| | last3 = Wyman
| |
| | first3 = Jeffreys
| |
| | title = On the existence of a steady state in a biological system
| |
| | journal = [[PNAS]]
| |
| | volume = 74
| |
| | pages = 4182–4184
| |
| | year = 1977a
| |
| | doi = 10.1073/pnas.74.10.4182
| |
| | issue = 10
| |
| | bibcode = 1977PNAS...74.4182F }}. A short research announcement reporting the results detailed in {{harv|Fichera|Sneider|Wyman|1977}}.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Numerical and quantitative analysis. Translated from Italian by Sandro Graffi
| |
| | place = London–San Francisco–Melbourne
| |
| | publisher = [[Pitman Publishing]]
| |
| | pages = x+208
| |
| | year = 1978a
| |
| | series = Surveys and Reference Works in Mathematics
| |
| | volume = 3
| |
| | mr = 0519677
| |
| | zbl = 0384.65043
| |
| | isbn = 0-273-00284-8
| |
| }}. An English updated [[translation]] of the memoir {{Harv|Fichera|1974a}}.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Un problema di analisi matematica proposto dalla biologia
| |
| | language = Italian
| |
| | journal = [[Rendiconti di Matematica e delle sue applicazioni]]
| |
| | series = 6
| |
| | volume = 10
| |
| | issue = 4
| |
| | pages = 1–6
| |
| | year = 1978b
| |
| | mr = 0503945
| |
| | zbl = 0378.34039
| |
| }}. "''A problem in mathematical analysis proposed by biology''" (English translation of the title) is a survey paper on an interdisciplinary research conducted by him, [[Maria Adelaide Sneider]] and [[Jeffries Wyman (biologist)|Jeffries Wyman]], on the existence of a [[steady state]] in a [[biological system]]: the research results were previously published as {{harv|Fichera|Sneider|Wyman|1977}}.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | author-link =
| |
| | title = Il contributo italiano alla teoria matematica dell'elasticità
| |
| | journal = [[Rendiconti del Circolo Matematico di Palermo]]
| |
| | language = Italian
| |
| | series = Serie II,
| |
| | volume = Tomo XXVIII
| |
| | date = January–April 1979
| |
| | issue = 1
| |
| | pages = 5–26
| |
| | doi = 10.1007/BF02849579
| |
| | mr = 0564544
| |
| | zbl = 0433.73002
| |
| }}. The address of Gaetano Fichera given on the occasion of the conferment of the [[laurea honoris causa]] in [[civil engineering]]: he describes the history of the theory of elasticity particularly detailing the contributions of Italian mathematicians and engineers.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Remarks on Saint-Venant's principle
| |
| | journal = [[Rendiconti di Matematica e delle sue applicazioni]]
| |
| | series = Serie 6
| |
| | volume = 12
| |
| | issue = 2
| |
| | pages = 181–200
| |
| | year = 1979a
| |
| | mr = 0557661
| |
| | zbl = 0443.73002
| |
| }}. A paper containing a mathematical proof of the [[Saint-Venant's principle]].
| |
| * {{citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Avere una memoria tenace crea gravi problem
| |
| | language = Italian
| |
| | journal = [[Archive for Rational Mechanics and Analysis]]
| |
| | volume = 70
| |
| | issue = 2
| |
| | year = 1979b
| |
| | pages = 373–387
| |
| | mr = 1553577
| |
| | zbl = 0425.73002
| |
| | doi = 10.1007/BF00281161
| |
| | bibcode = 1979ArRMA..70..373.
| |
| }}. "''Having a tenacious memory creates serious problems''" (English translation of the title) is a well known work on the [[fading memory principle]] and on the consequences implied by its not careful adoption.
| |
| *{{Citation
| |
| | first = Gaetano
| |
| | last = Fichera
| |
| | editor-last = Ansorge
| |
| | editor-first = R.
| |
| | editor2-last = Glashoff
| |
| | editor2-first = K.
| |
| | editor3-last = Werner
| |
| | editor3-first = B.
| |
| | contribution = The problem of the completeness of systems of particular solutions of partial differential equations
| |
| | title = Numerical mathematics, Symposium on the Occasion of Retirement of [[Lothar Collatz]], Hamburg 1979
| |
| | year = 1979c
| |
| | series = International Series of Numerical Mathematics
| |
| | volume = 49
| |
| | pages = 25–41
| |
| | place = [[Basel]]
| |
| | publisher=[[Birkhäuser-Verlag]]
| |
| | zbl = 0434.35010
| |
| }}.
| |
| *{{Citation
| |
| | first = Gaetano
| |
| | last = Fichera
| |
| | contribution = Problemi al contorno per le funzioni pluriarmoniche
| |
| | title = Atti del Convegno celebrativo dell'80° anniversario della nascita di Renato Calapso, [[Messina]]–[[Taormina]], 1–4 aprile 1981
| |
| | year = 1982a
| |
| | pages = 127–152
| |
| | language = Italian
| |
| | place = Roma
| |
| | publisher = Libreria Eredi Virgilio Veschi
| |
| | mr = 0698973
| |
| | zbl = 0958.32504
| |
| }}. In the work "''Boundary value problems for pluriharmonic functions''" (English translation of the title) a [[Trace operator|trace condition]] for [[pluriharmonic function]]s is proved.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Valori al contorno delle funzioni pluriarmoniche: estensione allo spazio <math>R^{2n}</math> di un teorema di L. Amoroso
| |
| | journal = [[Rendiconti del Seminario Matematico e Fisico di Milano]]
| |
| | volume = 52
| |
| | issue = 1
| |
| | pages = 23–34
| |
| | year = 1982b
| |
| | language = Italian
| |
| | doi = 10.1007/BF02924996
| |
| | mr = 0802991
| |
| | zbl= 0569.31006
| |
| }}. "''Boundary values of pluriharmonic functions: extension to the space <math>R^{2n}</math> of a theorem of L. Amoroso''" .
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Su un teorema di L. Amoroso nella teoria delle funzioni analitiche di due variabili complesse
| |
| | journal = [[Revue Roumaine de Mathématiques Pures et Appliquées]]
| |
| | volume = 27
| |
| | pages = 327–333
| |
| | year = 1982c
| |
| | language = Italian
| |
| | mr = 0669481
| |
| | zbl = 0509.31007
| |
| }}. In this paper, it is proved that a necessary and sufficient condition for an harmonic function defined on a [[Ball (mathematics)|ball]] in ℂ<sup>''2''</sup> to be pluriharmonic is to satisfy the [[Amoroso integral equation]]: an English translation of the title is:-"''On a theorem of L. Amoroso in the theory of analytic functions of two complex variables''.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Sul teorema di Cauchy–Morera per le funzioni analitiche di più variabili complesse
| |
| | language = Italian
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali]]
| |
| | series = Series VIII
| |
| | volume = 74
| |
| | issue = 6
| |
| | pages = 336–350
| |
| | year = 1983
| |
| | zbl = 0573.32005
| |
| }}. In the work "''On the theorem of Cauchy–Morera for analytic functions of several complex variables''" (English translation of the title), [[Morera's theorem]] for [[several complex variables|analytic functions of several complex variables]] is proved under the sole hypothesis of [[Locally integrable function|local integrability]] for the given function <math>f</math>.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Unification of global and local existence theorems for holomorphic functions of several complex variables
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Memorie. Classe di Scienze Fisiche, Matematiche e Naturali]]
| |
| | series = Serie VIII
| |
| | volume = 18
| |
| | issue = 3
| |
| | pages = 61–83
| |
| | year = 1986
| |
| | mr = 0917525
| |
| | zbl = 0705.32006
| |
| }}. A paper describing the ideas of {{Harv|Fichera|1957}}, giving some extensions of those ideas and a solution for a particular [[Cauchy problem]] for [[Several complex variables|holomorphic functions of several variables]].
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Ricordo di Renato Caccioppoli
| |
| | language = Italian
| |
| | journal = [[Ricerche di Matematica]]
| |
| | volume = 40
| |
| | issue = supplement
| |
| | pages = 11–15
| |
| | year = 1991
| |
| | zbl = 0788.01051
| |
| }}. Some of Fichera's recollections on his close friend [[Renato Caccioppoli]].
| |
| *{{citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | author-link =
| |
| | title = Il calcolo infinitesimale alle soglie del Duemila
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Supplemento]]
| |
| | volume = 4
| |
| | series = Serie IX,
| |
| | issue = 1
| |
| | year = 1993
| |
| | pages = 69–86
| |
| }}. "''Infinitesimal calculus at the threshold of the Millennium''" (English translation of the title)is a survey paper by Gaetano Fichera, describing the development of [[infinitesimal calculus]] during the twentieth century and trying to trace possible scenarios for its future evolution.
| |
| *{{citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = L'ultima lezione
| |
| | language = Italian
| |
| | journal = Rendiconti della Accademia Nazionale delle Scienze detta dei XL, Memorie di Matematica e Applicazioni
| |
| | volume = 19
| |
| | issue = 1
| |
| | year = 1995a
| |
| | pages = 1–24
| |
| | url= http://www.accademiaxl.it/Biblioteca/Pubblicazioni/browser.php?VoceID=2643
| |
| | mr= 1387547
| |
| }}. His "''last lesson''" of the course of higher analysis, given on the occasion of his retirement from university teaching in 1992.
| |
| *{{Citation
| |
| | first = Gaetano
| |
| | last = Fichera
| |
| | author-link =
| |
| | editor-last =
| |
| | editor-first =
| |
| | contribution = La nascita della teoria delle disequazioni variazionali ricordata dopo trent'anni
| |
| | title = Incontro scientifico italo-spagnolo. Roma, 21 ottobre 1993
| |
| | url = http://www.lincei.it/pubblicazioni/catalogo/volume.php?lg=e&rid=32885
| |
| | language = Italian
| |
| | year = 1995b
| |
| | pages = 47–53
| |
| | place = [[Rome|Roma]]
| |
| | series = Atti dei Convegni Lincei
| |
| | volume = 114
| |
| | publisher = [[Accademia Nazionale dei Lincei]]
| |
| }}. ''The birth of the theory of variational inequalities remembered thirty years later'' (English translation of the title) tell the story of the beginning of the theory of variational inequalities from the point of view of its founder.
| |
| *{{Citation
| |
| | first = Gaetano
| |
| | last = Fichera
| |
| | editor-last = Tarozzi
| |
| | editor-first = Gino
| |
| | contribution = Rivisitazione e storia due aspetti contrastanti della storiografia scientifica
| |
| | title = Convegno "Giuseppe Geminiani", Cesena 16–19 October 1995
| |
| | language = Italian
| |
| | year = 1996
| |
| | place = [[Cesena]]–[[Urbino]]
| |
| | pages =
| |
| }}. "''Revisiting and history: two conflicting aspects of scientific historiography''" details its author's opinions about the way of doing historical researches on mathematical topics.
| |
| *{{Citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = A boundary value problem connected with response of semi-space to a short laser pulse
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei, Rendiconti Lincei, Matematica e Applicazioni]]
| |
| | series = Serie IX,
| |
| | volume = 8
| |
| | issue = 4
| |
| | pages = 197–228
| |
| | year = 1997
| |
| | url = http://www.bdim.eu/item?id=RLIN_1997_9_8_3_197_0
| |
| | mr = 1611621
| |
| | zbl = 0903.35034
| |
| }}. Gaetano Fichera last, postumhous scientific paper, prepared for the publication by [[Olga Arsenievna Oleinik]] and his wife.
| |
| *{{citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Opere storiche biografiche, divulgative
| |
| | publisher= Giannini / [[Società Nazionale di Scienze, Lettere e Arti in Napoli]]
| |
| | location = [[Napoli]]
| |
| | year = 2002
| |
| | page = 491
| |
| | language = English and Italian
| |
| | url = http://www.socnazsla.unina.it/italiano/fismat/pubbl.htm
| |
| }}. Gaetano Fichera's "''Historical, biographical, expository works''": a volume collecting his contributions to the fields of [[history of mathematics]] and scientific expository work.
| |
| * {{citation
| |
| | last = Fichera
| |
| | first = Gaetano
| |
| | title = Opere scelte
| |
| | language = various languages
| |
| | publisher = Edizioni Cremonese (distributed by [[Unione Matematica Italiana]])
| |
| | place = [[Firenze]]
| |
| | year = 2004
| |
| | pages = XXIX+432 (vol. 1), pp. VI+570 (vol. 2), pp. VI+583 (vol. 3)
| |
| | language = Italian
| |
| | url =
| |
| | isbn =
| |
| }} ISBN 88-7083-811-0 (vol. 1), ISBN 88-7083-812-9 (vol. 2), ISBN 88-7083-813-7 (vol. 3). His "''Selected works''": three volumes collecting the most important mathematical papers of Gaetano Fichera, with a biographical sketch of [[Olga Arsenievna Oleinik|Olga A. Oleinik]]
| |
| | |
| == See also ==
| |
| *[[Constitutive equation]]s
| |
| *[[CR-function]]
| |
| *[[Hp-FEM#Example: the Fichera problem|Fichera corner problem]]
| |
| *[[Mauro Picone]]
| |
| *[[Potential theory]]
| |
| *[[Saint-Venant's principle]]
| |
| *[[Signorini problem]]
| |
| *[[Variational inequality]]
| |
| | |
| == Notes ==
| |
| {{Reflist|29em}}
| |
| | |
| == Biographical references ==
| |
| *{{citation
| |
| | last = Amerio
| |
| | first = Luigi
| |
| | author-link = Luigi Amerio
| |
| | title = Intervento
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Supplemento]]
| |
| | volume = 8
| |
| | series = Serie IX,
| |
| | issue = 1
| |
| | year = 1997
| |
| | pages = 15–16
| |
| }}. The "''Address''" (free English translation) of Amerio at the meeting "''Ricordo di Gaetano Fichera''" (English translation: "''Remembrance of Gaetano Fichera''") held in Rome at the Accademia Nazionale dei Lincei on the 8th of February 1997.
| |
| *{{Citation
| |
| | last = Antman
| |
| | first = Stuart
| |
| | title = The influence of elasticity in analysis: modern developments
| |
| | journal = [[Bulletin of the American Mathematical Society]]
| |
| | volume = 9
| |
| | issue = 3
| |
| | pages = 267–291
| |
| | year = 1983
| |
| | doi = 10.1090/S0273-0979-1983-15185-6
| |
| | mr = 714990
| |
| | zbl = 0533.73001
| |
| }}. A historical paper about the fruitful interaction of [[elasticity theory]] and [[mathematical analysis]]: the creation of the theory of [[variational inequalities]] by Fichera is described in paragraph 5, pages 282–284.
| |
| *{{citation
| |
| | last = Baiocchi
| |
| | first = Claudio
| |
| | author-link = Claudio Baiocchi
| |
| | title = Intervento
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Supplemento]]
| |
| | volume = 8
| |
| | series = Serie IX,
| |
| | issue = 1
| |
| | year = 1997
| |
| | pages = 17–18
| |
| }}. The "''Address''" (free English translation) of Baiocchi at the meeting "''Ricordo di Gaetano Fichera''" (English translation: "''Remembrance of Gaetano Fichera''") held in Rome at the Accademia Nazionale dei Lincei on the 8th of February 1997.
| |
| *{{citation
| |
| | last = Colautti Fichera
| |
| | first = Matelda
| |
| | title = Elenco delle pubblicazioni di Gaetano Fichera
| |
| | language = Italian
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Supplemento]]
| |
| | volume = 8
| |
| | series = 9
| |
| | issue = 1
| |
| | year = 1997
| |
| | pages = 14–33
| |
| }}. The "''List of the publications of Gaetano Fichera''", prepared by his wife as follow-up to the commemorative paper by Olga Oleinik ([[#{{harvid|Oleinik|1997}}|1997]]).
| |
| *{{Citation
| |
| | last = Colautti Fichera
| |
| | first = Matelda
| |
| | title = ... ed è subito sera... La lunga, brevissima vita di Gaetano Fichera
| |
| | place = Roma
| |
| | publisher = [[Self-published]]
| |
| | year = 2007
| |
| | page = 217
| |
| | language = Italian
| |
| }}. The story of the life of Gaetano Fichera written by his wife, Matelda Colautti Fichera. The first, untranslated phrase of the title is the last verse (and title) of a famous poem of [[Salvatore Quasimodo]], and was the concluding phrase of the last lesson of Fichera, in the occasion of his retirement from university teaching in 1992, published in {{Harv|Fichera|1995a}}, while a translation of the second phrase is:-"''The long, extremely short life of Gaetano Fichera''". There is also a free electronic edition with a different title: {{Citation
| |
| | last = Colautti Fichera
| |
| | first = Matelda
| |
| | title = Gaetano
| |
| | url =
| |
| | publisher = [[Lulu (company)|Lulu]]
| |
| | date = 30 September 2011
| |
| | page = 217
| |
| | language = Italian
| |
| }}.
| |
| *{{Citation
| |
| | last = Cosentini
| |
| | first = Cristofo
| |
| | author-link = Cristoforo Cosentini
| |
| | title = Ricordo del Prof. Gaetano Fichera, socio d'onore
| |
| | journal= [[Memorie e Rendiconti della Accademia di scienze, lettere e belle arti degli Zelanti e dei Dafnici]]
| |
| | series = Serie IV,
| |
| | volume = VI
| |
| | pages = 429–434
| |
| | language = Italian
| |
| | year = 1996
| |
| | url =
| |
| }}. "''Recollection of Prof. Gaetano Fichera, honorary member''" is a commemorative paper written by Cristoforo Cosentini, former member and president of the [[Accademia di scienze, lettere e belle arti degli Zelanti e dei Dafnici]] and close friend of Gaetano Fichera.
| |
| *{{Citation
| |
| | last = Galletto
| |
| | first = Dionigi
| |
| | title = Ricordo di Gaetano Fichera a dieci anni dalla morte
| |
| | journal = [[Atti Ufficiali dell'Accademia delle Scienze di Torino]]
| |
| | volume = 2004–2006
| |
| | pages = 135–142
| |
| | language = Italian
| |
| | year = 2007
| |
| | url = http://www.accademiadellescienze.it/media/679
| |
| }}, available from the [[Accademia delle Scienze di Torino]]. "''Recollection of Gaetano Fichera ten years after the death''": a commemoration written by one of the former students of [[Mauro Picone]], and colleague of Fichera as a member the Turin Academia.
| |
| *{{citation
| |
| | last = Grioli
| |
| | first = Giuseppe
| |
| | title = Ricordo di Gaetano Fichera
| |
| | journal = Rendiconti della Accademia Nazionale delle Scienze detta dei XL, Memorie di Matematica e Applicazioni
| |
| | volume = 20
| |
| | issue = 1
| |
| | series = Serie 5,
| |
| | year = 1996
| |
| | pages = 221–224
| |
| | language = Italian
| |
| | url= http://www.accademiaxl.it/Biblioteca/Pubblicazioni/browser.php?VoceID=2706
| |
| | mr = 1438747
| |
| | zbl = 0942.01023
| |
| }}. "''Remembrance of Gaetano Fichera''": the recollections of a friends and early colleague at the [[Istituto Nazionale per le Applicazioni del Calcolo]].
| |
| *{{citation
| |
| | last = Grioli
| |
| | first = Giuseppe
| |
| | author-link = Giuseppe Grioli
| |
| | title = Intervento
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Supplemento]]
| |
| | volume = 8
| |
| | series = Serie IX,
| |
| | issue = 1
| |
| | year = 1997
| |
| | pages = 19–20
| |
| }}. The "''Address''" (free English translation) of Grioli at the meeting "''Ricordo di Gaetano Fichera''" (English translation: "''Remembrance of Gaetano Fichera''") held in Rome at the Accademia Nazionale dei Lincei on 8 February 1997.
| |
| *{{Citation
| |
| | last = Kósa
| |
| | first = András
| |
| | author-link = András Kósa
| |
| | title = Mauro Picone e Gaetano Fichera / Mauro Picone és Gaetano Fichera
| |
| | journal = [[Italia & Italy]]
| |
| | volume = No. 28–29
| |
| | pages = 36–38
| |
| | date=January–April 2006
| |
| | language = Hungarian and Italian
| |
| | url = http://www.italcultbudapest.hu/Italia-Italy/Italia%20&%20Italy%20-%20Gen-Apr%202006/36-38.pdf
| |
| | doi =
| |
| | id =
| |
| | mr =
| |
| | zbl =
| |
| }}. The personal recollection of András Kósa on Gaetano Fichera and Mauro Picone.
| |
| *{{Citation
| |
| | last = Lax
| |
| | first = Peter
| |
| | author-link = Peter Lax
| |
| | editor-last = Mosco
| |
| | editor-first = Umberto
| |
| | editor-link = Umberto Mosco
| |
| | editor2-last = Ricci
| |
| | editor2-first = Paolo Emilio
| |
| | editor2-link = Paolo Emilio Ricci
| |
| | contribution = Thoughts on Gaetano Fichera
| |
| | title = Volume speciale in occasione dell'85-esimo anniversario della nascita di Gaetano Fichera
| |
| | place = Roma
| |
| | journal = Rendiconti della Accademia Nazionale delle Scienze detta dei XL. Memorie di Matematica e Applicazioni
| |
| | series = Serie V,
| |
| | volume = Vol. XXX
| |
| | issue = I
| |
| | origyear = 124<sup>o</sup>
| |
| | year = 2006
| |
| | pages = 1–2
| |
| | url =
| |
| | doi =
| |
| | id =
| |
| | isbn =
| |
| | mr = 2489588
| |
| }}.
| |
| *{{citation
| |
| | last = Malaroda
| |
| | first = Roberto
| |
| | author-link = Roberto Malaroda
| |
| | title = Intervento
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Supplemento]]
| |
| | volume = 8
| |
| | series = Serie IX,
| |
| | issue = 1
| |
| | year = 1997
| |
| | page = 22
| |
| }}. The "''Address''" (free English translation) of Malaroda at the meeting "''Ricordo di Gaetano Fichera''" (English translation: "''Remembrance of Gaetano Fichera''") held in Rome at the Accademia Nazionale dei Lincei on the 8th of February 1997.
| |
| *{{Citation
| |
| | last = Maz'ya
| |
| | first = Vladimir
| |
| | author-link = Vladimir Gilelevich Maz'ya
| |
| | title = Problemi attuali dell’analisi e della fisica matematica. Atti del II simposio internazionale (Taormina, 15–17 ottobre 1998). Dedicato alla memoria del Prof. Gaetano Fichera.
| |
| | editor-last = Ricci
| |
| | editor-first = Paolo Emilio
| |
| | editor-link = Paolo Emilio Ricci
| |
| | contribution = In memory of Gaetano Fichera
| |
| | year = 2000
| |
| | pages = 1–4
| |
| | place = [[Rome|Roma]]
| |
| | publisher = [[Aracne (publisher)|Aracne]]
| |
| | mr = 1809014
| |
| | zbl = 0977.01027
| |
| }}. Some vivid recollection about Fichera by [[Vladimir Gilelevich Maz'ya]].
| |
| *{{Citation
| |
| | last = Millán Gasca
| |
| | first = Ana
| |
| | author-link = Ana Maria Millán Gasca
| |
| | title = Gaetano Fichera (1922–1996)
| |
| | journal = Lettera dall'Italia
| |
| | volume = XI
| |
| | issue = 43–44
| |
| | pages = 114–115
| |
| | year = 1996
| |
| | month =
| |
| | language = Italian
| |
| | url =
| |
| | jstor =
| |
| }}.
| |
| *{{Citation
| |
| | last = Morawetz
| |
| | first = Cathleen S.
| |
| | author-link = Cathleen Synge Morawetz
| |
| | editor-last = Mosco
| |
| | editor-first = Umberto
| |
| | editor-link = Umberto Mosco
| |
| | editor2-last = Ricci
| |
| | editor2-first = Paolo Emilio
| |
| | editor2-link = Paolo Emilio Ricci
| |
| | contribution = A Memory of Gaetano Fichera
| |
| | title = Volume speciale in occasione dell'85-esimo anniversario della nascita di Gaetano Fichera
| |
| | place = Roma
| |
| | journal = Rendiconti della Accademia Nazionale delle Scienze detta dei XL. Memorie di Matematica e Applicazioni
| |
| | series = Serie V,
| |
| | volume = Vol. XXX
| |
| | issue = I
| |
| | origyear = 124<sup>o</sup>
| |
| | year = 2006
| |
| | pages = 3–6
| |
| | url =
| |
| | doi =
| |
| | id =
| |
| | isbn =
| |
| | mr = 2489589
| |
| }}.
| |
| *{{Citation
| |
| | last = Oleinik
| |
| | first = Olga A.
| |
| | authorlink = Olga Arsenievna Oleinik
| |
| | title = Problemi attuali dell’analisi e della fisica matematica. Atti del simposio internazionale dedicato a Gaetano Fichera nel suo 70<sup>o</sup> compleanno. [[Taormina]], 15–17 ottobre 1992
| |
| | editor-last = Ricci
| |
| | editor-first = Paolo Emilio
| |
| | editor-link = Paolo Emilio Ricci
| |
| | contribution = The Scientific work of Gaetano Fichera
| |
| | year = 1993
| |
| | pages = 7–29
| |
| | place = Roma
| |
| | publisher = Dipartimento di Matematica, Università di Roma "La Sapienza"
| |
| | mr = 1249085
| |
| | zbl = 0792.01033
| |
| }}.
| |
| *{{citation
| |
| | last = Oleinik
| |
| | first = Olga A.
| |
| | author-link = Olga Arsenievna Oleinik
| |
| | title = The life and scientific work of Gaetano Fichera
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Supplemento]]
| |
| | volume = 8
| |
| | series = Serie IX,
| |
| | issue = 1
| |
| | year = 1997
| |
| | pages = 9–14
| |
| }}. The biographical sketch of Fichera by [[Olga Arsenievna Oleinik|Olga Oleinik]]at the meeting "''Ricordo di Gaetano Fichera''" (English translation: "''Remembrance of Gaetano Fichera''") held in Rome at the Accademia Nazionale dei Lincei on the 8th of February 1997. The same paper is also included in the first volume of the selected works of Gaetano Fichera ([[#{{harvid|Fichera|2004}}|2004]]) and in the volume of his historical, biographical, and expository works ([[#{{harvid|Fichera|2002}}|2002]]).*{{Citation
| |
| | last = Pagani
| |
| | first = Antonio
| |
| | author-link =
| |
| | title = E' café d'Cai
| |
| | place = [[Alfonsine]]
| |
| | publisher = La Voce del Senio
| |
| | year = 2005
| |
| | page = 126
| |
| | language = Italian
| |
| | url = http://alfonsinemonamour.racine.ra.it/alfonsine/Alfonsine/Cafe%20d%20cai/Antonio%20Pagani%20Cai.htm
| |
| | id =
| |
| | isbn =
| |
| }}. This book offers the personal recollections of the Author about the life in his birthplace [[Alfonsine]], during the [[Italian fascism|fascist period]] up to the end of [[World War II]]. He describes various episodes of the life of Gaetano Fichera in his town during wartime, their friendship and the relations between Fichera and the [[Italian resistance movement]]. The choice of photographies and the presentation of the book are due to Luciano Lucci, who also cured the web edition which is enriched by several pictures at the expense of the loss of printed edition pagination. The first part of the title, up to the [[Colon (punctuation)|colon]], is in [[Emiliano-Romagnolo]] and means "''Cai's [[Café]]''" where ''Cai'' is the nickname of the Author's family, while the second part is in Italian and its English translation reads as:-"''the adventures of a young man in Alfonsine during fascism''".
| |
| *{{Citation
| |
| | last = Presidenza della Repubblica Italiana
| |
| | author-link =
| |
| | title = Medaglia d'oro ai benemeriti della scuola della cultura e dell'arte: Gaetano Fichera
| |
| | date = July 31, 1973
| |
| | url = http://www.quirinale.it/elementi/DettaglioOnorificenze.aspx?decorato=6951
| |
| | accessdate = May 31, 2011
| |
| }}.
| |
| *{{Citation
| |
| | last = Ricci
| |
| | first = Paolo E.
| |
| | author-link = Paolo Emilio Ricci
| |
| | title = Scomparsa del Prof. Gaetano Fichera
| |
| | journal = [[Notiziario dell'Unione Matematica Italiana]]
| |
| | volume = XXIII
| |
| | issue = 6
| |
| | pages = 48–50
| |
| | date = June 1996
| |
| }}.
| |
| *{{Citation
| |
| | last = Ricci
| |
| | first = P. E.
| |
| | author-link = Paolo Emilio Ricci
| |
| | last2 = Gilbert
| |
| | first2 = R. P.
| |
| | author2-link = Robert Pertsch Gilbert
| |
| | title = A Short Biography of Gaetano Fichera
| |
| | journal = [[Applicable Analysis]]
| |
| | volume = 65
| |
| | issue = 1–2
| |
| | pages = 1–2
| |
| | year = 1997
| |
| | doi = 10.1080/00036819708840545
| |
| | mr = 1674583
| |
| | zbl = 0973.01037
| |
| }}.
| |
| *{{Citation
| |
| | last = Rivlin
| |
| | first = R. S.
| |
| | author-link = Ronald Rivlin
| |
| | title = Biography. Gaetano Fichera
| |
| | journal = [[Applicable Analysis]]
| |
| | volume = 15
| |
| | issue = 1–4
| |
| | pages = 3–3
| |
| | year = 1983
| |
| | doi = 10.1080/00036818308839435
| |
| | mr = 0710179
| |
| | zbl = 0511.01010
| |
| }}.
| |
| *{{Citation
| |
| | last = Salvini
| |
| | first = Giorgio
| |
| | authorlink = Giorgio Salvini
| |
| | title = Problemi attuali dell’analisi e della fisica matematica. Atti del simposio internazionale dedicato a Gaetano Fichera nel suo 70<sup>o</sup> compleanno. [[Taormina]], 15–17 ottobre 1992
| |
| | editor-last = Ricci
| |
| | editor-first = Paolo Emilio
| |
| | editor-link = Paolo Emilio Ricci
| |
| | contribution = Saluto a Gaetano Fichera, nel suo 70<sup>o</sup> compleanno
| |
| | year = 1993
| |
| | pages = 1–6
| |
| | place = Roma
| |
| | publisher = Dipartimento di Matematica, Università di Roma "La Sapienza"
| |
| }}.
| |
| *{{citation
| |
| | last = Salvini
| |
| | first = Giorgio
| |
| | author-link = Giorgio Salvini
| |
| | title = Parole di saluto
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Supplemento]]
| |
| | volume = 8
| |
| | series = Serie IX,
| |
| | issue = 1
| |
| | year = 1997
| |
| | pages = 5–6
| |
| }}. The "''Salutation address''" (free English translation) of Salvini at the meeting "''Ricordo di Gaetano Fichera''" (English translation: "''Remembrance of Gaetano Fichera''") held in Rome at the Accademia Nazionale dei Lincei on the 8th of February 1997.
| |
| *{{Citation
| |
| | last = Vernacchia-Galli
| |
| | first = Jole
| |
| | author-link =
| |
| | title = Regesto delle lauree honoris causa dal 1944 al 1985
| |
| | place = Roma
| |
| | publisher = Edizioni Dell'Ateneo
| |
| | series = Studi e Fonti per la storia dell'Università di Roma
| |
| | volume = 10
| |
| | year = 1986
| |
| | chapter = [[José Luis Massera]]
| |
| | chapterurl =
| |
| | pages = 559–605
| |
| | language = Italian and [[Spanish language|Castilian]]
| |
| | url =
| |
| | doi =
| |
| | id =
| |
| | isbn =
| |
| }}. The "''regest of honoris causa degrees from 1944 to 1985''" (English translation of the title) is a detailed and carefully commented regest of all the documents of the official archive of the Sapienza University of Rome pertaining to the [[honoris causa]] [[Academic degree|degrees]], awarded or not. It includes all the awarding proposals submitted during the considered period, detailed presentations of the work of the candidate, if available, and precise references to related articles published on Italian newspapers and magazines, if the [[laurea]] was awarded.
| |
| *{{Citation
| |
| | last = Vernacchia-Galli
| |
| | first = Jole
| |
| | author-link =
| |
| | title = Regesto delle lauree honoris causa dal 1944 al 1985
| |
| | place = Roma
| |
| | publisher = Edizioni Dell'Ateneo
| |
| | series = Studi e Fonti per la storia dell'Università di Roma
| |
| | volume = 10
| |
| | year = 1986
| |
| | chapter = [[Andrei Sakharov|Andrej Dmitrievich Sakharov]]
| |
| | chapterurl =
| |
| | pages = 687–779
| |
| | language = Italian
| |
| | url =
| |
| | doi =
| |
| | id =
| |
| | isbn =
| |
| }}. The "''regest of honoris causa degrees from 1944 to 1985''" (English translation of the title) is a detailed and carefully commented regest of all the documents of the official archive of the Sapienza University of Rome pertaining to the honoris causa degrees, awarded or not. It includes all the awarding proposals submitted during the considered period, detailed presentations of the work of the candidate, if available, and precise references to related articles published on Italian newspapers and magazines, if the laurea was awarded.
| |
| *{{Citation
| |
| | last = Vernacchia-Galli
| |
| | first = Jole
| |
| | author-link =
| |
| | title = Regesto delle lauree honoris causa dal 1944 al 1985
| |
| | place = Roma
| |
| | publisher = Edizioni Dell'Ateneo
| |
| | series = Studi e Fonti per la storia dell'Università di Roma
| |
| | volume = 10
| |
| | year = 1986
| |
| | chapter = [[Fritz John]]
| |
| | chapterurl =
| |
| | pages = 823–844
| |
| | language = Italian
| |
| | url =
| |
| | doi =
| |
| | id =
| |
| | isbn =
| |
| }}. The "''regest of honoris causa degrees from 1944 to 1985''" (English translation of the title) is a detailed and carefully commented regest of all the documents of the official archive of the Sapienza University of Rome pertaining to the honoris causa degrees, awarded or not. It includes all the awarding proposals submitted during the considered period, detailed presentations of the work of the candidate, if available, and precise references to related articles published on Italian newspapers and magazines, if the laurea was awarded.
| |
| *{{Citation
| |
| | last = Vernacchia-Galli
| |
| | first = Jole
| |
| | author-link =
| |
| | title = Regesto delle lauree honoris causa dal 1944 al 1985
| |
| | place = Roma
| |
| | publisher = Edizioni Dell'Ateneo
| |
| | series = Studi e Fonti per la storia dell'Università di Roma
| |
| | volume = 10
| |
| | year = 1986
| |
| | chapter = [[Olga Arsenievna Oleinik]]
| |
| | chapterurl =
| |
| | pages = 845–855
| |
| | language = Italian
| |
| | url =
| |
| | doi =
| |
| | id =
| |
| | isbn =
| |
| }}. The "''regest of honoris causa degrees from 1944 to 1985''" (English translation of the title) is itself a detailed and carefully commented regest of all the documents of the official archive of the Sapienza University of Rome pertaining to the honoris causa degrees, awarded or not. It includes all the awarding proposals submitted during the considered period, detailed presentations of the work of the candidate, if available, and precise references to related articles published on Italian newspapers and magazines, if the [[laurea]] was awarded.
| |
| *{{citation
| |
| | last = Vesentini
| |
| | first = Edoardo
| |
| | author-link = Edoardo Vesentini
| |
| | title = Intervento
| |
| | journal = [[Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Supplemento]]
| |
| | volume = 8
| |
| | series = Serie IX,
| |
| | issue = 1
| |
| | year = 1997
| |
| | page = 21
| |
| }}. The "''Address''" (free English translation) of Vesentini at the meeting "''Ricordo di Gaetano Fichera''" (English translation: "''Remembrance of Gaetano Fichera''") held in Rome at the Accademia Nazionale dei Lincei on the 8th of February 1997.
| |
| *{{Citation
| |
| | last = Wendland
| |
| | first = Wolfgang L.
| |
| | title = In memory of Gaetano Fichera
| |
| | journal = [[Le Matematiche]]
| |
| | volume = LXII
| |
| | issue = II
| |
| | pages = 7–9
| |
| | year = 2007
| |
| | url = http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/24
| |
| | mr = 2401174
| |
| }}. Some recollections of the author about Gaetano Fichera.
| |
| *{{Citation
| |
| | first = Henrik
| |
| | last = Zorski
| |
| | author-link =
| |
| | editor-last = Capriz
| |
| | editor-first = Gianfranco
| |
| | editor-link =
| |
| | editor2-last = Grioli
| |
| | editor2-first = Giuseppe
| |
| | editor2-link = Giuseppe Grioli
| |
| | editor3-last = Manacorda
| |
| | editor3-first = Tristano
| |
| | editor3-link = Tristano Manacorda
| |
| | contribution = Gaetano Fichera and ISIMM (International Society for Interaction between Analysis and Mechanics)
| |
| | title = Interactions between Analysis and Mechanics. The Legacy of Gaetano Fichera. Convegno internazionale (Roma, 22--23 aprile 1998)
| |
| | year = 1999
| |
| | pages = 11–17
| |
| | place = [[Rome|Roma]]
| |
| | series = Atti dei Convegni Lincei
| |
| | volume = 148
| |
| | publisher = [[Accademia Nazionale dei Lincei]]
| |
| | url=http://www.lincei.it/pubblicazioni/catalogo/volume.php?lg=e&rid=36500
| |
| }}. A biographical work focusing on the contributions of Gaetano Fichera to [[mechanics]] and the role played by him in the founding of the [[International Society for Interaction between Analysis and Mechanics|ISIMM]].
| |
| | |
| == References ==
| |
| *{{Citation
| |
| | last = Amoroso
| |
| | first = Luigi
| |
| | author-link = Luigi Amoroso
| |
| | title = Sopra un problema al contorno (About a boundary value problem)
| |
| | journal = [[Rendiconti del Circolo Matematico di Palermo]]
| |
| | language = Italian
| |
| | volume = 33
| |
| | issue = 1
| |
| | pages = 75–85
| |
| | year = 1912
| |
| | doi = 10.1007/BF03015289
| |
| | jfm = 43.0453.03
| |
| }}. The first paper where a set of (fairly complicate) necessary and sufficient conditions for the solvability of the [[Dirichlet problem]] for [[Several complex variables|holomorphic functions of several variables]] is given: the [[bounded set|bounded]] [[Domain (mathematics)#Real and complex analysis|domain]] where the problem is posed and solved is assumed to be not [[pseudoconvexity|pseudoconvex]].
| |
| *{{Citation
| |
| | last = Bochner
| |
| | first = Salomon
| |
| | author-link = Salomon Bochner
| |
| | title = The theorem of Morera in several variables
| |
| | journal = [[Annali di Matematica Pura e Applicata]]
| |
| | volume = 34
| |
| | issue = 1
| |
| | pages = 27–39
| |
| | year = 1953
| |
| | doi = 10.1007/BF02415323
| |
| | zbl = 0052.30703
| |
| }}.
| |
| *{{Citation
| |
| | editor-last = Bonafede
| |
| | editor-first = S.
| |
| | editor2-last = Cialdea
| |
| | editor2-first = A.
| |
| | editor2-link = Alberto Cialdea
| |
| | editor3-last = Germano
| |
| | editor3-first = B.
| |
| | editor4-last = Laforgia
| |
| | editor4-first = A.
| |
| | editor5-last = Ricci.
| |
| | editor5-first = P. E.
| |
| | editor5-link = Paolo Emilio Ricci
| |
| | title = 3<sup>o</sup> Simposio Internazionale Problemi Attuali dell'Analisi e della Fisica Matematica, dedicato alla memoria di Gaetano Fichera – Taormina, 29 Giugno–1 Luglio 2006
| |
| | journal = [[Le Matematiche]]
| |
| | volume = LXII
| |
| | issue = II
| |
| | year = 2007
| |
| | url = http://www.dmi.unict.it/ojs/index.php/lematematiche/issue/view/4
| |
| | zbl = 1139.74400
| |
| }}. A volume of the journal published by the Mathematics Department of the [[University of Catania]], containing a selection of papers presented to the ''3rd international symposium on current problems in analysis and mathematical physics dedicated to Gaetano Fichera'', a periodic conference dedicated to Gaetano Fichera.
| |
| *{{Citation
| |
| | last = Cafiero
| |
| | first = Federico
| |
| | author-link = Federico Cafiero
| |
| | title = Misura e integrazione
| |
| | place = [[Rome|Roma]]
| |
| | publisher = Edizioni Cremonese
| |
| | year = 1959
| |
| | series = Monografie matematiche del [[Consiglio Nazionale delle Ricerche]]
| |
| | volume = 5
| |
| | pages = VII+451
| |
| | id =
| |
| | mr = 0215954
| |
| | zbl = 0171.01503
| |
| | language = Italian
| |
| }}. ''Measure and integration'' (as the English translation of the title reads) is a definitive monograph on integration and measure theory: the treatment of the limiting behavior of the integral of various kind of [[sequences]] of measure-related structures (measurable functions, [[measurable set]]s, measures and their combinations) is somewhat conclusive.
| |
| *{{Citation
| |
| | first =
| |
| | last =
| |
| | author-link =
| |
| | editor-last = Capriz
| |
| | editor-first = Gianfranco
| |
| | editor-link =
| |
| | editor2-last = Grioli
| |
| | editor2-first = Giuseppe
| |
| | editor2-link = Giuseppe Grioli
| |
| | editor3-last = Manacorda
| |
| | editor3-first = Tristano
| |
| | editor3-link = Tristano Manacorda
| |
| | contribution =
| |
| | title = Interactions between Analysis and Mechanics. The Legacy of Gaetano Fichera. Convegno internazionale (Roma, 22--23 aprile 1998)
| |
| | year = 1999
| |
| | pages = 148
| |
| | place = [[Rome|Roma]]
| |
| | series = Atti dei Convegni Lincei
| |
| | volume = 148
| |
| | publisher = [[Accademia Nazionale dei Lincei]]
| |
| | url=http://www.lincei.it/pubblicazioni/catalogo/volume.php?lg=e&rid=36500
| |
| }}.
| |
| *{{Citation
| |
| | first =
| |
| | last =
| |
| | author-link =
| |
| | first2 =
| |
| | last2 =
| |
| | author2-link =
| |
| | editor-last = Cialdea
| |
| | editor-first = Alberto
| |
| | editor-link = Alberto Cialdea
| |
| | title = Homage to Gaetano Fichera
| |
| | contribution =
| |
| | contribution-url =
| |
| | series = quaderni di matematica
| |
| | volume = 7
| |
| | year = 2000
| |
| | pages = xiv+347
| |
| | language = English and Italian
| |
| | place = Rome
| |
| | publisher = [[Aracne (publisher)|Aracne]]
| |
| | url = http://www.dimat.unina2.it/quaderni/quaderni07.htm
| |
| | doi =
| |
| | id =
| |
| | mr = 1913523
| |
| | zbl = 0982.00057
| |
| }}. A volume published by the [[Department of mathematics]] the [[Seconda Università degli Studi di Napoli]] in its journal "''[[Quaderni di matematica]]''", dedicated to the memory of Gaetano Fichera: the contributions, written by his pupils, friends and collaborators, deal about topics that inspired Fichera's scientific work.
| |
| *{{Citation
| |
| | last = Günther
| |
| | first = Nikolai Maximovich
| |
| | author-link = Nikolai Maximovich Günther
| |
| | title = Potential theory and its applications to basic problems of mathematical physics
| |
| | place = New York
| |
| | publisher = [[Frederick Ungar Publishing]]
| |
| | year = 1967
| |
| | url =
| |
| | zbl = 0164.41901
| |
| | isbn = }}. A classical textbook in [[potential theory]]: paragraph 24 of chapter const of results proved by Gaetano Fichera in {{Harv|Fichera|1948}}.
| |
| *{{Citation
| |
| | last =
| |
| | first =
| |
| | author-link =
| |
| | last2 =
| |
| | first2 =
| |
| | author2-link =
| |
| | editor-last = Mosco
| |
| | editor-first = Umberto
| |
| | editor-link = Umberto Mosco
| |
| | editor2-last = Ricci
| |
| | editor2-first = Paolo Emilio
| |
| | editor2-link = Paolo Emilio Ricci
| |
| | title = Volume speciale in occasione dell'85-esimo anniversario della nascita di Gaetano Fichera
| |
| | place = Roma
| |
| | journal = Rendiconti della Accademia Nazionale delle Scienze detta dei XL. Memorie di Matematica e Applicazioni
| |
| | series = Serie V,
| |
| | volume = Vol. XXX
| |
| | issue = I
| |
| | origyear = 124<sup>o</sup>
| |
| | year = 2006
| |
| | pages = X+228
| |
| | url =
| |
| | doi =
| |
| | id =
| |
| | isbn =
| |
| | mr =
| |
| | zbl =
| |
| }}. This is a volume dedicated to Gaetano Fichera on the occasion of his 85th birthday anniversary, and "''contains contributions by several scientists outside Italy, who knew Fichera personally, either through working with him, or through his work''", as remarked by the editors on page VII.
| |
| *{{Citation
| |
| | editor-last = Kiguradze
| |
| | editor-first = Ivan
| |
| | editor2-last = Shervashidze
| |
| | editor2-first = Tengiz
| |
| | title = Issue dedicated to the memory of Prof. Gaetano Fichera (1922–1996) on the occasion of his 85th birthday
| |
| | journal = [[Georgian Mathematical Journal]]
| |
| | volume = 14
| |
| | issue = 1
| |
| | year = 2007
| |
| | url = http://www.degruyter.com/view/j/gmj.2007.14.issue-1/issue-files/gmj.2007.14.issue-1.xml
| |
| }}. Published by the A. Razmadze Mathematical Institute of the [[Georgian National Academy of Sciences]].
| |
| *{{citation
| |
| | last = Range
| |
| | first = R. Michael
| |
| | title = Extension phenomena in multidimensional complex analysis: correction of the historical record
| |
| | journal = [[The Mathematical Intelligencer]]
| |
| | volume = 24
| |
| | issue = 2
| |
| | year = 2002
| |
| | pages = 4–12
| |
| | doi = 10.1007/BF03024609
| |
| | mr = 1907191
| |
| }}. An historical paper correcting some inexact historical statements in the theory of [[Several complex variables|holomorphic functions of several variables]], particularly concerning contributions of Gaetano Fichera and [[Francesco Severi]].
| |
| *{{citation
| |
| | last = Range
| |
| | first = R. Michael
| |
| | title = Some landmarks in the history of the tangential Cauchy Riemann equations
| |
| | journal = [[Rendiconti di Matematica e delle Sue Applicazioni]]
| |
| | volume = 30
| |
| | issue = 3–4
| |
| | year = 2010
| |
| | pages = 275–283
| |
| | url = http://www.mat.uniroma1.it/ricerca/rendiconti/2010%283-4%29/275-283.pdf
| |
| | doi =
| |
| | mr = 2830305
| |
| | zbl = 1233.32023
| |
| }}. An historical paper exploring further the same topic previously dealt in the paper {{harv|Range|2002}} by the same author.
| |
| *{{Citation
| |
| | last =
| |
| | first =
| |
| | authorlink =
| |
| | title = Problemi attuali dell’analisi e della fisica matematica. Atti del simposio internazionale dedicato a Gaetano Fichera nel suo 70<sup>o</sup> compleanno. [[Taormina]], 15–17 ottobre 1992
| |
| | editor-last = Ricci
| |
| | editor-first = Paolo Emilio
| |
| | editor-link = Paolo Emilio Ricci
| |
| | contribution =
| |
| | year = 1993
| |
| | pages = x+252
| |
| | place = Roma
| |
| | publisher = Dipartimento di Matematica, Università di Roma "La Sapienza"
| |
| | mr = 1249083
| |
| | zbl = 0786.00028
| |
| }}.
| |
| *{{Citation
| |
| | last = Severi
| |
| | first = Francesco
| |
| | author-link = Francesco Severi
| |
| | title = Sur une propriété fondamentale des fonctions analytiques de plusieurs variables
| |
| | journal=[[Comptes rendus de l'Académie des sciences#1835-1965|Comptes rendus hebdomadaires des séances de l'Académie des sciences]]
| |
| | volume = 192
| |
| | pages = 596–599
| |
| | year = 1931
| |
| | url = http://gallica.bnf.fr/ark:/12148/bpt6k3145g.image.r=Comptes+rendus.f596.langFR
| |
| | zbl = 0001.14802
| |
| }}, available at [[Gallica]].
| |
| *{{Citation
| |
| | last = Severi
| |
| | first = Francesco
| |
| | author-link = Francesco Severi
| |
| | title = Lezioni sulle funzioni analitiche di più variabili complesse – Tenute nel 1956–57 all'Istituto Nazionale di Alta Matematica in [[Rome|Roma]]
| |
| | place = Padova
| |
| | publisher = CEDAM – Casa Editrice Dott. Antonio Milani
| |
| | year = 1958
| |
| | pages = XIV+255
| |
| | language = Italian
| |
| | url =
| |
| | doi =
| |
| | id =
| |
| | zbl= 0094.28002
| |
| | isbn = }}. Notes from a course held by Francesco Severi at the [[Istituto Nazionale di Alta Matematica]] (which at present is named after him), containing appendices of [[Enzo Martinelli]], [[Giovanni Battista Rizza]] and [[Mario Benedicty]]. An English translation of the title reads as:-"''Lectures on analytic functions of several complex variables – Lectured in 1956–57 at the Istituto Nazionale di Alta Matematica in Rome''".
| |
| *{{Citation
| |
| | first = Hans F.
| |
| | last = Weinberger
| |
| | author-link = Hans Weinberger
| |
| | editor-last = Capriz
| |
| | editor-first = Gianfranco
| |
| | editor-link =
| |
| | editor2-last = Grioli
| |
| | editor2-first = Giuseppe
| |
| | editor2-link = Giuseppe Grioli
| |
| | editor3-last = Manacorda
| |
| | editor3-first = Tristano
| |
| | editor3-link = Tristano Manacorda
| |
| | contribution = Fichera's method for bounding eigenvalues
| |
| | title = Interactions between Analysis and Mechanics. The Legacy of Gaetano Fichera. Convegno internazionale (Roma, 22--23 aprile 1998)
| |
| | year = 1999
| |
| | pages = 51–65
| |
| | place = [[Rome|Roma]]
| |
| | series = Atti dei Convegni Lincei
| |
| | volume = 148
| |
| | publisher = [[Accademia Nazionale dei Lincei]]
| |
| | url =http://www.lincei.it/pubblicazioni/catalogo/volume.php?lg=e&rid=36500
| |
| }}. (See here [http://www.math.umn.edu/~hfw/Math/fichera981102.ps] for a [[preprint]] version available from the Author's website retrieved on 1 May 2009). An expository paper detailing the contributions of Gaetano Fichera and his school on the problem of numerical calculation of [[eigenvalue]]s for general [[differential operator]]s.
| |
| | |
| == External links ==
| |
| *{{MathGenealogy|id=126413|title=Gaetano Fichera}}
| |
| *{{MacTutor| id=Fichera | title=Gaetano Fichera | date= July 2012}}
| |
| *{{Citation
| |
| | contribution = Fichèra, Gaetano
| |
| | title = [[Enciclopedia Treccani]]
| |
| | language = Italian
| |
| | year = 2008
| |
| | url = http://www.treccani.it/enciclopedia/gaetano-fichera/
| |
| | accessdate = 14 April 2011}}. The biographical entry about Gaetano Fichera at the [[Enciclopedia Treccani]].
| |
| | |
| {{Use dmy dates|date=September 2011}}
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| | |
| {{Authority control|VIAF=21151959}}
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| | |
| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| |
| | NAME = Fichera, Gaetano
| |
| | ALTERNATIVE NAMES =
| |
| | SHORT DESCRIPTION = Italian mathematician
| |
| | DATE OF BIRTH = 8 February 1922
| |
| | PLACE OF BIRTH = [[Acireale]]
| |
| | DATE OF DEATH = 1 June 1996
| |
| | PLACE OF DEATH = Rome
| |
| }}
| |
| {{DEFAULTSORT:Fichera, Gaetano}}
| |
| [[Category:1922 births]]
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| [[Category:1996 deaths]]
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| [[Category:People from Acireale]]
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| [[Category:20th-century Italian mathematicians]]
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| [[Category:Complex analysts]]
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| [[Category:Historians of mathematics]]
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| [[Category:Mathematical analysts]]
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| [[Category:Mathematical physicists]]
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| [[Category:PDE theorists]]
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| [[Category:Sicilian mathematicians]]
| |