The Classical Moment Problem and Generalized Indefinite Strings

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Abstract

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 \(2\times 2\) canonical systems with Hamburger Hamiltonians.

Keywords

Hamburger moment problem Generalized indefinite strings 

Mathematics Subject Classification

Primary 44A60 34L05 Secondary 34B20 34B07 

Notes

Acknowledgements

Open access funding provided by Austrian Science Fund (FWF).

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria
  2. 2.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia
  3. 3.RUDN UniversityMoscowRussia

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