Etudes for the inverse spectral problem

Nikolai Makarov; Alexei Poltoratski

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arXiv · 2204.08395

Etudes for the inverse spectral problem

Nikolai Makarov·Alexei Poltoratski

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Abstract

In this note we study inverse spectral problems for canonical Hamiltonian systems, which encompass a broad class of second order differential equations on a half-line. Our goal is to extend the classical resultss developed in the work of Marchenko, Gelfand-Levitan, and Krein to broader classes of canonical systems and to illustrate the solution algorithms and formulas with a variety of examples. One of the main ingredients of our approach is the use of truncated Toeplitz operators, which complement the standard toolbox of the Krein-de Branges theory of canonical systems.

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BibTeX RIS

Nikolai Makarov, Alexei Poltoratski. 2022-04-18. Etudes for the inverse spectral problem. https://arxiv.org/abs/2204.08395

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