Talk:Hamburger moment problem

Can't be right
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 $$\mu_n$$ 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)

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)