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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2017 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2017
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149264 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862723712973799424 |
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| author | Zagorodnyuk, S.M. |
| author_facet | Zagorodnyuk, S.M. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T18:43:15Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149264 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:43:15Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | The Inverse Spectral Problem for Jacobi-Type Pencils Zagorodnyuk, S.M. |
| title | 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_short | The Inverse Spectral Problem for Jacobi-Type Pencils |
| title_sort | inverse spectral problem for jacobi-type pencils |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149264 |
| work_keys_str_mv | AT zagorodnyuksm theinversespectralproblemforjacobitypepencils AT zagorodnyuksm inversespectralproblemforjacobitypepencils |