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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2017 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2017
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149264 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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. |
Institution
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. |
| work_keys_str_mv |
AT zagorodnyuksm theinversespectralproblemforjacobitypepencils AT zagorodnyuksm inversespectralproblemforjacobitypepencils |
| first_indexed |
2025-12-07T18:43:15Z |
| last_indexed |
2025-12-07T18:43:15Z |
| _version_ |
1850876096286818304 |