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Periodic GMP matrices

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Periodic GMP matrices. / Eichinger, Benjamin.
In: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), Vol. 12, 066, 07.07.2016.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Eichinger, B 2016, 'Periodic GMP matrices', Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), vol. 12, 066. https://doi.org/10.3842/SIGMA.2016.066

APA

Eichinger, B. (2016). Periodic GMP matrices. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 12, Article 066. https://doi.org/10.3842/SIGMA.2016.066

Vancouver

Eichinger B. Periodic GMP matrices. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2016 Jul 7;12:066. doi: 10.3842/SIGMA.2016.066

Author

Eichinger, Benjamin. / Periodic GMP matrices. In: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2016 ; Vol. 12.

Bibtex

@article{6362fee1893a49daa6a3771e0997b7b2,
title = "Periodic GMP matrices",
abstract = "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.",
keywords = "Bases of rational functions, Functional models, Periodic Jacobi matrices, Spectral theory",
author = "Benjamin Eichinger",
note = "Publisher Copyright: {\textcopyright} 2016, Institute of Mathematics. All rights reserved.",
year = "2016",
month = jul,
day = "7",
doi = "10.3842/SIGMA.2016.066",
language = "English",
volume = "12",
journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",
issn = "1815-0659",
publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

}

RIS

TY - JOUR

T1 - Periodic GMP matrices

AU - Eichinger, Benjamin

N1 - Publisher Copyright: © 2016, Institute of Mathematics. All rights reserved.

PY - 2016/7/7

Y1 - 2016/7/7

N2 - 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.

AB - 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.

KW - Bases of rational functions

KW - Functional models

KW - Periodic Jacobi matrices

KW - Spectral theory

U2 - 10.3842/SIGMA.2016.066

DO - 10.3842/SIGMA.2016.066

M3 - Journal article

AN - SCOPUS:84984832187

VL - 12

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

M1 - 066

ER -