Hall's universal group

In mathematics, particularly, in analysis, Carleman's condition gives a sufficient condition for the determinacy of the moment problem. That is, if a measure μ satisfies Carleman's condition, there is no other measure ν having the same moments as μ. The condition was discovered by Torsten Carleman in 1922.

Hamburger moment problem

For the Hamburger moment problem (the moment problem on the whole real line), the theorem states the following:

Let μ be a measure on R such that all the moments

$m_n=\underset{-\mathrm{\infty }}{\overset{+\mathrm{\infty }}{\int }}{x}^{n}d\mu (x),n=0,1,2,\cdots$

are finite. If

$\sum _{n=1}^{\mathrm{\infty }}{m}_{2n}^{-\frac{1}{2n}}=+\mathrm{\infty },$

then the moment problem for m_n is determinate; that is, μ is the only measure on R with (m_n) as its sequence of moments.

Stieltjes moment problem

For the Stieltjes moment problem, the sufficient condition for determinacy is Template:Clarify

$\sum _{n=1}^{\mathrm{\infty }}{m}_n^{-\frac{1}{2n}}=+\mathrm{\infty }.$

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

References

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534