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arXiv · 1707.08394

The Classical Moment Problem and Generalized Indefinite Strings

Jonathan Eckhardt·Aleksey Kostenko
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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.

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Jonathan Eckhardt, Aleksey Kostenko. 2017-07-26. The Classical Moment Problem and Generalized Indefinite Strings. https://doi.org/10.1007/s00020-018-2446-6

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