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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| Дата: | 2016 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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
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irk-123456789-1477632019-02-16T01:26:11Z Periodic GMP Matrices Eichinger, B. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147763 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Eichinger, B. |
| spellingShingle |
Eichinger, B. Periodic GMP Matrices Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Eichinger, B. |
| author_sort |
Eichinger, B. |
| title |
Periodic GMP Matrices |
| title_short |
Periodic GMP Matrices |
| title_full |
Periodic GMP Matrices |
| title_fullStr |
Periodic GMP Matrices |
| title_full_unstemmed |
Periodic GMP Matrices |
| title_sort |
periodic gmp matrices |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147763 |
| citation_txt |
Periodic GMP Matrices / B. Eichinger // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT eichingerb periodicgmpmatrices |
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2023-05-20T17:28:30Z |
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2023-05-20T17:28:30Z |
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1796153382562430976 |