Periodic GMP Matrices
We recall criteria on the spectrum of Jacobi matrices such that the corresponding isospectral torus consists of periodic operators. Motivated by those known results for Jacobi matrices, we define a new class of operators called GMP matrices. They form a certain Generalization of matrices related to...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2016 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2016
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147763 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Periodic GMP Matrices / B. Eichinger // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862574631028785152 |
|---|---|
| author | Eichinger, B. |
| author_facet | Eichinger, B. |
| citation_txt | Periodic GMP Matrices / B. Eichinger // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We recall criteria on the spectrum of Jacobi matrices such that the corresponding isospectral torus consists of periodic operators. Motivated by those known results for Jacobi matrices, we define a new class of operators called GMP matrices. They form a certain Generalization of matrices related to the strong Moment Problem. This class allows us to give a parametrization of almost periodic finite gap Jacobi matrices by periodic GMP matrices. Moreover, due to their structural similarity we can carry over numerous results from the direct and inverse spectral theory of periodic Jacobi matrices to the class of periodic GMP matrices. In particular, we prove an analogue of the remarkable ''magic formula'' for this new class.
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| first_indexed | 2025-11-26T10:10:01Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147763 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T10:10:01Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Eichinger, B. 2019-02-15T19:16:00Z 2019-02-15T19:16:00Z 2016 Periodic GMP Matrices / B. Eichinger // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 30E05; 30F15; 47B36; 42C05; 58J53 DOI:10.3842/SIGMA.2016.066 https://nasplib.isofts.kiev.ua/handle/123456789/147763 We recall criteria on the spectrum of Jacobi matrices such that the corresponding isospectral torus consists of periodic operators. Motivated by those known results for Jacobi matrices, we define a new class of operators called GMP matrices. They form a certain Generalization of matrices related to the strong Moment Problem. This class allows us to give a parametrization of almost periodic finite gap Jacobi matrices by periodic GMP matrices. Moreover, due to their structural similarity we can carry over numerous results from the direct and inverse spectral theory of periodic Jacobi matrices to the class of periodic GMP matrices. In particular, we prove an analogue of the remarkable ''magic formula'' for this new class. This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications.
 The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html.
 The author was supported by the Austrian Science Fund FWF, project no: P25591-N25. He
 would like to thank his advisor Peter Yuditskii for his guidance and help during the preparation
 of this paper. Finally, he is grateful to the anonymous referees for their remarks that improved
 the presentation of the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Periodic GMP Matrices Article published earlier |
| spellingShingle | Periodic GMP Matrices Eichinger, B. |
| title | Periodic GMP Matrices |
| title_full | Periodic GMP Matrices |
| title_fullStr | Periodic GMP Matrices |
| title_full_unstemmed | Periodic GMP Matrices |
| title_short | Periodic GMP Matrices |
| title_sort | periodic gmp matrices |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147763 |
| work_keys_str_mv | AT eichingerb periodicgmpmatrices |