Talk:Hamburger moment problem

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I don't think that the second characterisation can be right: consider a distribution whose mean is zero so that \Delta_1^{(1)}=-\mu_2^2.

According to The Moment Problem, which looks authoritative, this characterisation is actually the solution to the Stieltjes moment problem, and the wikipedia article on that is only a stub.

So I propose to move this condition to the Stiltjes problem page.

Meanwhile, again according to The Moment Problem the solution to the Hamburger moment problem is that the sequence μn should be positive definite. It is not completely obvious to me that that is equivalent to this characterisation 1, it feels stronger. Can anyone confirm or otherwise?

Kestrelsummer 22:33, 17 January 2007 (UTC)

[edit] parametrization of solutions

i think the statement "the solutions of the Hamburger moment problem is parametrized by the self-adjoint extensions of the operator T" is correct and should be retained. so a necessary and sufficient condition that the solution is unique is that the deficiency index of T-bar, the closure of the operator T, be (0,0), which is quite nice. Mct mht 01:27, 29 September 2007 (UTC)

Actually, I'm puzzled why this correspondence was removed. It seems very natural and a nice application of the theory of extensions of symmetric operators.--CSTAR 02:12, 2 October 2007 (UTC)