On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. I. General Case
In the context of dissipative and accumulative di erential equations (which contain the spectral parameter λ nonlinearly) in a separable Hilbert space H we introduce a characteristic operator M(λ) that works as an analog of the characteristic Weyl-Titchmarsh matrix. Its existence and properties are...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2006 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106589 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. I. General Case / V.I. Khrabustovsky // Журнал математической физики, анализа, геометрии. — 2006. — Т. 2, № 2. — С. 149-175. — Бібліогр.: 31 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862726082548989952 |
|---|---|
| author | Khrabustovsky, V.I. |
| author_facet | Khrabustovsky, V.I. |
| citation_txt | On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. I. General Case / V.I. Khrabustovsky // Журнал математической физики, анализа, геометрии. — 2006. — Т. 2, № 2. — С. 149-175. — Бібліогр.: 31 назв. — англ. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| description | In the context of dissipative and accumulative di erential equations (which contain the spectral parameter λ nonlinearly) in a separable Hilbert space H we introduce a characteristic operator M(λ) that works as an analog of the characteristic Weyl-Titchmarsh matrix. Its existence and properties are investigated. A description of M(λ) that corresponds to separated boundary conditions is given. Analogs for Weyl functions and solutions are introduced. Weyl type inequalities for those analogs are established, which reduce to well-known inequalities in various special cases. The proofs are based on description and properties of maximal semi-definite subspaces in H² of special form that we provide while studying boundary problems for equations as above.
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| first_indexed | 2025-12-07T18:55:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106589 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T18:55:45Z |
| publishDate | 2006 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Khrabustovsky, V.I. 2016-09-30T20:37:36Z 2016-09-30T20:37:36Z 2006 On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. I. General Case / V.I. Khrabustovsky // Журнал математической физики, анализа, геометрии. — 2006. — Т. 2, № 2. — С. 149-175. — Бібліогр.: 31 назв. — англ. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106589 In the context of dissipative and accumulative di erential equations (which contain the spectral parameter λ nonlinearly) in a separable Hilbert space H we introduce a characteristic operator M(λ) that works as an analog of the characteristic Weyl-Titchmarsh matrix. Its existence and properties are investigated. A description of M(λ) that corresponds to separated boundary conditions is given. Analogs for Weyl functions and solutions are introduced. Weyl type inequalities for those analogs are established, which reduce to well-known inequalities in various special cases. The proofs are based on description and properties of maximal semi-definite subspaces in H² of special form that we provide while studying boundary problems for equations as above. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. I. General Case Article published earlier |
| spellingShingle | On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. I. General Case Khrabustovsky, V.I. |
| title | On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. I. General Case |
| title_full | On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. I. General Case |
| title_fullStr | On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. I. General Case |
| title_full_unstemmed | On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. I. General Case |
| title_short | On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. I. General Case |
| title_sort | on the characteristic operators and projections and on the solutions of weyl type of dissipative and accumulative operator systems. i. general case |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106589 |
| work_keys_str_mv | AT khrabustovskyvi onthecharacteristicoperatorsandprojectionsandonthesolutionsofweyltypeofdissipativeandaccumulativeoperatorsystemsigeneralcase |