On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications

We construct a functional model (direct integral expansion) and study the spectra of certain periodic block-operator Jacobi matrices, in particular, of general 2D partial difference operators of the second order. We obtain the upper bound, optimal in a sense, for the Lebesgue measure of their spectr...

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Бібліографічні деталі
Опубліковано в:Symmetry, Integrability and Geometry: Methods and Applications
Дата:2019
ISSN:1815-0659
Автори: Golinskii, L., Kutsenko, A.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2019
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/210172
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications / L. Golinskii, A. Kutsenko // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 12 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Golinskii, L.
Kutsenko, A.
author_facet Golinskii, L.
Kutsenko, A.
citation_txt On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications / L. Golinskii, A. Kutsenko // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 12 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We construct a functional model (direct integral expansion) and study the spectra of certain periodic block-operator Jacobi matrices, in particular, of general 2D partial difference operators of the second order. We obtain the upper bound, optimal in a sense, for the Lebesgue measure of their spectra. The examples of the operators for which there are several gaps in the spectrum are given.
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language English
last_indexed 2025-12-07T21:24:37Z
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publisher Інститут математики НАН України
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spelling Golinskii, L.
Kutsenko, A.
2025-12-03T14:23:42Z
2019
On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications / L. Golinskii, A. Kutsenko // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 12 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 47B36; 47B39; 35P15
arXiv: 1809.07136
https://nasplib.isofts.kiev.ua/handle/123456789/210172
https://doi.org/10.3842/SIGMA.2019.050
We construct a functional model (direct integral expansion) and study the spectra of certain periodic block-operator Jacobi matrices, in particular, of general 2D partial difference operators of the second order. We obtain the upper bound, optimal in a sense, for the Lebesgue measure of their spectra. The examples of the operators for which there are several gaps in the spectrum are given.
We thank the anonymous referees for their valuable remarks, which improved the paper significantly.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications
Article
published earlier
spellingShingle On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications
Golinskii, L.
Kutsenko, A.
title On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications
title_full On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications
title_fullStr On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications
title_full_unstemmed On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications
title_short On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications
title_sort on direct integral expansion for periodic block-operator jacobi matrices and applications
url https://nasplib.isofts.kiev.ua/handle/123456789/210172
work_keys_str_mv AT golinskiil ondirectintegralexpansionforperiodicblockoperatorjacobimatricesandapplications
AT kutsenkoa ondirectintegralexpansionforperiodicblockoperatorjacobimatricesandapplications