T-matrix method: Difference between revisions

Latest revision as of 08:59, 7 April 2013

In mathematics, orthogonal polynomials on the unit circle are families of polynomials that are orthogonal with respect to integration over the unit circle in the complex plane, for some probability measure on the unit circle. They were introduced by Template:Harvs.

Definition

Suppose that μ is a probability measure on the unit circle in the complex plane, whose support is not finite. The orthogonal polynomials associated to μ are the polynomials Φ_n(z) with leading coefficients zⁿ that are orthogonal with respect to the measure μ.

The Szegő recurrence

Szegő's recurrence states that

Φ_{n + 1} (z) = z Φ_{n} (z) - {\overline{α}}_{n} Φ_{n}^{*} (z)

where

Φ_{n}^{*} (z) = z^{n} \overline{Φ_{n} (\overset{- 1}{\overline{z}})}

is the polynomial with its coefficients reversed and complex conjugated, and where the Verblunsky coefficients α_n are complex numbers with absolute values less than 1.

Verblunsky's theorem

Verblunsky's theorem states that any sequence of complex numbers in the open unit disk is the sequence of Verblunsky coefficients for a unique probability measure on the unit circle with infinite support.

Geronimus's theorem

Geronimus's theorem states that the Verblunsky coefficients of the measure μ are the Schur parameters of the function f defined by the equations

\frac{1 + z f (z)}{1 - z f (z)} = F (z) = \int \frac{e^{i θ} + z}{e^{i θ} - z} d μ .

Baxter's theorem

Baxter's theorem states that the Verblunsky coefficients form an absolutely convergent series if and only if the moments of μ form an absolutely convergent series and the weight function w is strictly positive everywhere.

Szegő's theorem

Szegő's theorem states that

\prod (1 - | α_{j} |^{2}) = \exp (\int_{0}^{2 π} \log (w (θ)) d θ / 2 π)

where wdθ/2π is the absolutely continuous part of the measure μ.

Rakhmanov's thoerem

Rakhmanov's theorem states that if the absolutely continuous part w of the measure μ is positive almost everywhere then the Verblunsky coefficients α_n tend to 0.

Examples

The Rogers–Szegő polynomials are an example of orthogonal polynomials on the unit circle.

References

Template:Dlmf
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

@@ Line 1: / Line 1: @@
-Whenever operating it, if you use the Facebook version of the Clash of Lords you will require link with the internet. We produced this unique special tool dealing with a universal hacking system for Facebook and iOs games therefore we custom-made it so that you can make use of Clash of Lords main repository. [http://tinyurl.com/q38lk2a download clash of lords 2 hack] New Clash of Lords 2 Hack Tool for Android and iOS for unlimited amount of Gold, Jewels and additional Potions. This specific conflict of Lords zero price hack program is very easily portable and it is probably just take significantly less than 1 minute to down load it, also on a slower web connection. Being down load a file from FileIce you have to finish a fast review, it is a type of researching the market.<br><br>Act as the best possible lord of this planet by making use of within the online game conflict of Lords 2 a plan to find and that is Clash of Lords 2 Hack cost-free Gather your military and plan war in conflict of Lords 2 APK The war among the events of beasts and personal knowledge tactic mayhem unlike what you've ever played prior to! Although utilizing the totally free Jewels because precisely as Cost-totally no-cost platinum regarding Clash of Lords two it really is doable to fundamentally obtain anything you desire from your task.<br><br>Other major qualities for this hack device include producing capable account for dragon soldiers, and upgrade the city hall towards the subsequent amount. conflict of Lords online game is a excellent game as well as the hack tool may have many features like including endless silver, jewels, speedup the dragon soldiers and has now a straightforward style for several people.<br><br>Conflict of lords hack is the most recent on-line game where the people can perform numerous activities with magic to obtain the tactic showdown is Clash of Lords. All of that is done possible by indicates for the Clash of Lords 2 Hack Application. Underneath you can view point by signifies of point information about the Clash related to Lords two Cheats, the way the product functions and additionally a bit evidence image. To relax and play this game everyone need to down load the conflict of lords hack device which helps to get more things. Using the real totally free Jewels and free of charge of charge Gold pertaining to Clash connected with Lords 2 it is possible to in an over-all feeling obtain all of that you necessitate from the real redirection.<br><br>However, you will be reminded every so often that no matter if Clash of Lords 2 is absolve to play game, it really is however a company and therefore if you want to be a high player, you have to throw in your wallet. Our Clash of Lords 2 Hack will help you in getting among the best players by giving you accessibility unlimited jewels, endless gold, unlimited souls and limitless bands! Clash of Lords 2 hack tool is brand-new program developed by GameSoftEmpire.<br><br>If you have any inquiries regarding which and tips on how to use clash of lords 2 jewels hack , you are going to be in a position to speak to us inside net internet site. Our teams at GS24 ltd tend to be pleasued to introduce the newest hack for conflict of Lords 2 ! Our tool is thouroughly tested exceptionally cautiously and then we be sure it operates a hundredpercent. In next words i'll provide training (for use and install software) photos that hack plus the hack functions. We could guarantee this hack will astonish you! Com shows the modern Clash of Lords two Cheats , the most up-to-date variation available to you online.<br><br>utilizing this totally free Jewelry and free silver designed for conflict of Lords 2 you should basically get what you may desire in the online game. Clash of Lords 2 Hack offers amazing choices to it's individual. Ideal tip that i've ever got in one great gamer ended up being that you will don't ever spend your personal money on this online cellular game because with the device that we shared for you, you could get limitless quantity of resources when you require them or want them. When you haven't played this game then chances are you must visit today in the Android or even the ions online software's store. A foremost load of redirection people have actually effectively used a Clash of Lords 2 hack whatever the case we'ven't yet!<br><br>Thank you for visiting all who will be wondering simple tips to cheat in Clash Of Lords 2 game. Episode 6 for Clash of Lords 2 from my buddy. Time spent to hack Clash of Lords 2 with this particular tool is minimal while the strategy is pretty safe. Clash of Lords 2 hack grab is simple and you just should follow simple directions an individual will be in the process. Method that will produce even more Jewels,Gold and souls you'll previously require is the Clash of Lords 2 hack. By using this Clash of Lords 2 Jewels hack you stay invisible and anonymous.<br><br>Indeed beyond any doubt, we found a great device that's called Clash of Lords 2 online hack for no-cost possessions and all sorts of various things in diversion when you need to. The tool is truly simple to make use of and contains an incredibly protected security and protection so that you will never get a restrict or obstructed through the diversion or Twitter. They couldn't believe less about money they just personality regarding best way of  be first-in the Clash of Lords 2. inspite of the way that you can expect to make use of a hack for Clash of Lords 2 it won't allow you to a great deal. I trust that you carefully enjoyed examining this unprecedented article about Clash of Lords 2 hack and cheats gizmo that could be affirmed anywhere from the best web inquiry products.<br><br>When you beloved this article along with you would want to acquire more info concerning [http://tinyurl.com/q38lk2a download clash of lords 2 hack] generously go to the web site.
+In mathematics, '''orthogonal polynomials on the unit circle''' are families of [[Orthogonal polynomials|polynomials that are orthogonal with respect to integration]] over the [[unit circle]] in the [[complex plane]], for some [[probability measure]] on the unit circle. They were  introduced  by {{harvs|txt|last=Szegő|year1=1920|year2=1921|year3=1939}}.
+==Definition==
+Suppose that μ is a probability measure on the unit circle in the complex plane, whose support is not finite. The orthogonal polynomials associated to μ are the polynomials Φ<sub>''n''</sub>(''z'') with leading coefficients ''z''<sup>''n''</sup> that are orthogonal with respect to the measure μ.
+==The Szegő recurrence ==
+Szegő's recurrence states that
+:<math>\Phi_{n+1}(z)=z\Phi_n(z)-\overline\alpha_n\Phi_n^*(z)</math>
+where
+:<math>\Phi_n^*(z)=z^n\overline{\Phi_n(\overline{z}^{-1})}</math>
+is the polynomial with its coefficients reversed and complex conjugated, and where the '''Verblunsky coefficients''' α<sub>''n''</sub> are complex numbers with absolute values less than 1.
+==Verblunsky's theorem==
+Verblunsky's theorem states that any sequence of complex numbers in the open unit disk is the sequence of Verblunsky coefficients for a unique probability measure on the unit circle with infinite support.
+==Geronimus's theorem==
+Geronimus's theorem states that the Verblunsky coefficients of the measure μ are the [[Schur parameters]] of the function ''f'' defined by the equations
+:<math> \frac{1+zf(z)}{1-zf(z)}=F(z)=\int\frac{e^{i\theta}+z}{e^{i\theta}-z}d\mu.</math>
+==Baxter's theorem==
+Baxter's theorem states that the Verblunsky coefficients form an absolutely convergent series if and only if the moments of μ form an absolutely convergent series and the weight function ''w'' is strictly positive everywhere.
+==Szegő's theorem==
+Szegő's theorem states that
+:<math>\prod(1-|\alpha_j|^2) = \exp\big(\int_0^{2\pi}\log(w(\theta))d\theta/2\pi\big)</math>
+where ''wd''θ/2π is the absolutely continuous part of the measure μ.
+==Rakhmanov's thoerem==
+Rakhmanov's theorem states that if the absolutely continuous part ''w'' of the measure μ is positive almost everywhere then the Verblunsky coefficients α<sub>''n''</sub> tend to 0.
+==Examples==
+The [[Rogers–Szegő polynomials]] are an example of orthogonal polynomials on the unit circle.
+==References==
+*{{dlmf|id=18.33|title=Orthogonal Polynomials on the unit circle|first=Tom H. |last=Koornwinder|first2=Roderick S. C.|last2= Wong|first3=Roelof |last3=Koekoek||first4=René F. |last4=Swarttouw}}
+*{{Citation | last1=Simon | first1=Barry | author1-link=Barry Simon | title=Orthogonal polynomials on the unit circle. Part 1. Classical theory | url=http://books.google.com/books?id=d94r7kOSnKcC | publisher=[[American Mathematical Society]] | location=Providence, R.I. | series=American Mathematical Society Colloquium Publications | isbn=978-0-8218-3446-6 | mr=2105088 | year=2005 | volume=54}}
+*{{Citation | last1=Simon | first1=Barry | author1-link=Barry Simon | title=Orthogonal polynomials on the unit circle. Part 2. Spectral theory | url=http://books.google.com/books?id=54juCPc3ulwC | publisher=[[American Mathematical Society]] | location=Providence, R.I. | series=American Mathematical Society Colloquium Publications | isbn=978-0-8218-3675-0 | mr=2105089 | year=2005 | volume=54}}
+*{{Citation | last1=Szegő | first1=Gábor | title=Beiträge zur Theorie der Toeplitzschen Formen | url=http://dx.doi.org/10.1007/BF01199955 | publisher=Springer Berlin / Heidelberg | doi=10.1007/BF01199955 | year=1920 | journal=[[Mathematische Zeitschrift]] | issn=0025-5874 | volume=6 | pages=167–202}}
+*{{Citation | last1=Szegő | first1=Gábor | title=Beiträge zur Theorie der Toeplitzschen Formen | url=http://dx.doi.org/10.1007/BF01279027 | publisher=Springer Berlin / Heidelberg | doi=10.1007/BF01279027 | year=1921 | journal=[[Mathematische Zeitschrift]] | issn=0025-5874 | volume=9 | pages=167–190}}
+*{{Citation | last1=Szegő | first1=Gábor | title=Orthogonal Polynomials | url=http://books.google.com/books?id=3hcW8HBh7gsC | publisher= American Mathematical Society | series=Colloquium Publications | isbn=978-0-8218-1023-1 | mr=0372517 | year=1939 | volume=XXIII}}
+[[Category:Orthogonal polynomials]]

T-matrix method: Difference between revisions

Latest revision as of 08:59, 7 April 2013

Contents

Definition

The Szegő recurrence

Verblunsky's theorem

Geronimus's theorem

Baxter's theorem

Szegő's theorem

Rakhmanov's thoerem

Examples

References

Navigation menu

T-matrix method: Difference between revisions

Latest revision as of 08:59, 7 April 2013

Definition

The Szegő recurrence

Verblunsky's theorem

Geronimus's theorem

Baxter's theorem

Szegő's theorem

Rakhmanov's thoerem

Examples

References

Navigation menu

Search