Backward extensions and strong Hamburger moment sequences (Q1193061)

A double sequence \(C:=\{c_ n: n=0,\pm 1,\pm 2,\dots\}\) of real numbers is called a strong Hamburger moment sequence (SHMS) if the strong Hamburger moment problem has a solution. The authors establish necessary and sufficient conditions for this solution to be essentially unique; i.e. the SHMS to be determinate. They start with the facts that \(C\) is a SHMS if and only if the classical Hamburger moment problem for \(C_ m:=\{c_{n- 2m}: n=0,1,2,\dots\}\) is solvable for every integer \(m\), and that \(C\) is determinate if there is an integer \(m\) such that \(C_ m\) is determinate. On the basis of this they characterize determinate SHMS in various ways.