The Classical Moment Problem and Generalized Indefinite Strings

We show that the classical Hamburger moment problem can be included in the spectral theory of generalized indefinite strings. More precisely, we introduce the class of Krein–Langer strings and show that there is a bijective correspondence between moment sequences and this class of generalized indefinite strings. This result can be viewed as a complement to the classical results of Krein on the connection between the Stieltjes moment problem and Krein–Stieltjes strings and Kac on the connection between the Hamburger moment problem and 2×2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\times 2$$\end{document} canonical systems with Hamburger Hamiltonians.