The Inverse Spectral Problem for Jacobi-Type Pencils

In this paper we study the inverse spectral problem for Jacobi-type pencils. By a Jacobi-type pencil we mean the following pencil J₅−λJ₃, where J₃ is a Jacobi matrix and J₅ is a semi-infinite real symmetric five-diagonal matrix with positive numbers on the second subdiagonal. In the case of a specia...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2017
Main Author: Zagorodnyuk, S.M.
Format: Article
Language:English
Published: Інститут математики НАН України 2017
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/149264
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:The Inverse Spectral Problem for Jacobi-Type Pencils / S.M. Zagorodnyuk // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 16 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-149264
record_format dspace
spelling Zagorodnyuk, S.M.
2019-02-19T19:31:38Z
2019-02-19T19:31:38Z
2017
The Inverse Spectral Problem for Jacobi-Type Pencils / S.M. Zagorodnyuk // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 16 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 42C05; 47B36
DOI:10.3842/SIGMA.2017.085
https://nasplib.isofts.kiev.ua/handle/123456789/149264
In this paper we study the inverse spectral problem for Jacobi-type pencils. By a Jacobi-type pencil we mean the following pencil J₅−λJ₃, where J₃ is a Jacobi matrix and J₅ is a semi-infinite real symmetric five-diagonal matrix with positive numbers on the second subdiagonal. In the case of a special perturbation of orthogonal polynomials on a finite interval the corresponding spectral function takes an explicit form.
This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications (OPSFA14). The full collection is available at https://www.emis.de/journals/SIGMA/OPSFA2017.html. The author is grateful to referees for their valuable comments and suggestions which led to an essential improvement of the paper.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
The Inverse Spectral Problem for Jacobi-Type Pencils
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title The Inverse Spectral Problem for Jacobi-Type Pencils
spellingShingle The Inverse Spectral Problem for Jacobi-Type Pencils
Zagorodnyuk, S.M.
title_short The Inverse Spectral Problem for Jacobi-Type Pencils
title_full The Inverse Spectral Problem for Jacobi-Type Pencils
title_fullStr The Inverse Spectral Problem for Jacobi-Type Pencils
title_full_unstemmed The Inverse Spectral Problem for Jacobi-Type Pencils
title_sort inverse spectral problem for jacobi-type pencils
author Zagorodnyuk, S.M.
author_facet Zagorodnyuk, S.M.
publishDate 2017
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description In this paper we study the inverse spectral problem for Jacobi-type pencils. By a Jacobi-type pencil we mean the following pencil J₅−λJ₃, where J₃ is a Jacobi matrix and J₅ is a semi-infinite real symmetric five-diagonal matrix with positive numbers on the second subdiagonal. In the case of a special perturbation of orthogonal polynomials on a finite interval the corresponding spectral function takes an explicit form.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/149264
citation_txt The Inverse Spectral Problem for Jacobi-Type Pencils / S.M. Zagorodnyuk // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 16 назв. — англ.
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first_indexed 2025-12-07T18:43:15Z
last_indexed 2025-12-07T18:43:15Z
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