Unique solvability of an extended Hamburger moment problem
R-functions are rational functions with no poles in the extended complex plane outside a given set \(\{a_ 1,...,a_ p\}\) of points on the real axis. Methods from the theory of orthogonal polynomials can be extended to R-functions. By this means the author solved an extended Hamburger moment problem: Given sequences of real numbers \(\{c_ n^{(i)}:n=1,2,...\}\), \(i=1,...,p\), find conditions for a distribution function \(\psi\) to exist such that \(\int^{\infty}_{-\infty}d\psi (t)=1,\quad \int^{\infty}_{-\infty}d\psi (t)/(t-a_ i)^ m=c_ m^{(i)},\) \(m=1,2,...,i=1,...,p\). In this paper these methods are extended to treat conditions for the moment problem to have a unique solution. The results are related to the classical limit point-limit circle situation.
scientific article; zbMATH DE number 4067558