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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2019 |
| ISSN: | 1815-0659 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2019
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| Online Zugang: | 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 |
| Zitieren: | 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| _version_ | 1862745363954270208 |
|---|---|
| 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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| first_indexed | 2025-12-07T21:24:37Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210172 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:37Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| 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 |