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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2023, Volume 20, Issue 2, Pages 1026–1036
DOI: https://doi.org/10.33048/semi.2023.20.063 (Mi semr1626) 		 
Real, complex and functional analysis

Inverse spectral problem for an antisymmetric tridiagonal matrix

A. I. Gudimenko

Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, ul. Radio, 7, 690041, Vladivostok, Russia
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DOI: https://doi.org/10.33048/semi.2023.20.063
Abstract: The problem of recovering an antisymmetric tridiagonal matrix from the eigenvalues of this matrix and the normalizing constants for its eigenvectors is solved. Matrices of this type arise in the theory of small oscillations of mechanical systems and are related to the matrices of the systems through the Schrödinger transformation. The problem is solved by the method of orthogonal polynomials.
Keywords: inverse spectral problem, antisymmetric tridiagonal matrix, Schrödinger variables.
Received February 26, 2023, published November 12, 2023
Document Type: Article
UDC: 517.984
MSC: 15A29,34A55,47B36
Language: Russian
Citation: A. I. Gudimenko, “Inverse spectral problem for an antisymmetric tridiagonal matrix”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 1026–1036
Citation in format AMSBIB
\Bibitem{Gud23}
\by A.~I.~Gudimenko
\paper Inverse spectral problem for an antisymmetric tridiagonal matrix
\jour Sib. \`Elektron. Mat. Izv.
\yr 2023
\vol 20
\issue 2
\pages 1026--1036
\mathnet{http://mi.mathnet.ru/semr1626}
\crossref{https://doi.org/10.33048/semi.2023.20.063}
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