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Periodic GMP Matrices

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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Main Author: Eichinger, B.
Format: Article
Language:English
Published: Інститут математики НАН України 2016
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/147763
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spelling 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
work_keys_str_mv AT eichingerb periodicgmpmatrices
first_indexed 2023-05-20T17:28:30Z
last_indexed 2023-05-20T17:28:30Z
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