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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2019 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210172 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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| ISSN: | 1815-0659 |