The Classical Moment Problem and Generalized Indefinite Strings

Abstract

We show that the classical Hamburger moment problem can be included in the spectral theory of generalized indefinite strings. Namely, 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 M. G. Krein on the connection between the Stieltjes moment problem and Krein-Stieltjes strings and I. S. Kac on the connection between the Hamburger moment problem and 2x2 canonical systems with Hamburger Hamiltonians.

25 pages

References in corpus (3)

• On an integrable two-component Camassa-Holm shallow water system
• An isospectral problem for global conservative multi-peakon solutions of the Camassa-Holm equation
• Real-valued algebro-geometric solutions of the two-component Camassa-Holm hierarchy

Cited by in corpus (10)

• A view of the peakon world through the lens of approximation theory
• The inverse spectral problem for periodic conservative multi-peakon solutions of the Camassa-Holm equation
• On the absolutely continuous spectrum of generalized indefinite strings
• Heat kernels of the discrete Laguerre operators
• Continued fraction expansions of Herglotz-Nevanlinna functions and generalized indefinite strings of Stieltjes type
• Trace formulas and inverse spectral theory for generalized indefinite strings
• On the absolutely continuous spectrum of generalized indefinite strings II
• On the solution of the inverse problem for a class of canonical systems corresponding to matrix string equations
• Inverse problems for finite Jacobi matrices and Krein--Stieltjes strings
• The conservative Camassa-Holm flow with step-like irregular initial data