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...
Збережено в:
| Дата: | 2006 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2006
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/106589 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-106589 |
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irk-123456789-1065892016-10-01T03:02:14Z 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. 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. 2006 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/106589 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Khrabustovsky, V.I. |
| spellingShingle |
Khrabustovsky, V.I. On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. I. General Case Журнал математической физики, анализа, геометрии |
| author_facet |
Khrabustovsky, V.I. |
| author_sort |
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_short |
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_sort |
on the characteristic operators and projections and on the solutions of weyl type of dissipative and accumulative operator systems. i. general case |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106589 |
| 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. |
| series |
Журнал математической физики, анализа, геометрии |
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2023-10-18T20:13:16Z |
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