Etudes for the inverse spectral problem
Spectral Theory
2023-05-25 v4
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.
Cite
@article{arxiv.2204.08395,
title = {Etudes for the inverse spectral problem},
author = {Nikolai Makarov and Alexei Poltoratski},
journal= {arXiv preprint arXiv:2204.08395},
year = {2023}
}