The many faces of the stochastic zeta function

Valkó, Benedek; Virág, Bálint

doi:10.1007/s00039-022-00613-8

Cited by 3 publications

(1 citation statement)

References 27 publications

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“…At present, the Krein-de Branges (KdB) theory became a standard tool in the area of spectral problems. The theory experiences a new peak of popularity in the last 20 years due to its connections to other areas such as the theory of orthogonal polynomials, number theory, random matrices and the nonlinear Fourier transform [1,2,6,8,14,16,17,29,34]. In addition to the original book by de Branges [7] and a chapter in the book by Dym and McKean [10], more recent monographs by Remling [31] and Romanov [32] contain the basics of KdB-theory and further references.…”

Section: Introductionmentioning

confidence: 99%

Etudes for the inverse spectral problem

Makarov

Poltoratski

2023

Journal of London Math Soc

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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 results developed in the work of Marchenko, Gelfand–Levitan, and Krein to broader classes of canonical systems and to illustrate the solution algorithms and formulae 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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