On Linear Relations Generated by a DiRerential Expression and by a Nevanlinna Operator Function
The families of maximal and minimal relations generated by a differential expression with bounded operator coe±cients and by a Nevanlinna operator function are defined. These families are proved to be holomorphic. In the case of finite interval, the space of boundary values is constructed. In terms...
Збережено в:
| Дата: | 2011 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2011
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/106668 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On Linear Relations Generated by a DiRerential Expression and by a Nevanlinna Operator Function / V.M. Bruk // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 2. — С. 115-140. — Бібліогр.: 25 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-106668 |
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dspace |
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irk-123456789-1066682016-10-02T03:03:04Z On Linear Relations Generated by a DiRerential Expression and by a Nevanlinna Operator Function Bruk, V.M. The families of maximal and minimal relations generated by a differential expression with bounded operator coe±cients and by a Nevanlinna operator function are defined. These families are proved to be holomorphic. In the case of finite interval, the space of boundary values is constructed. In terms of boundary conditions, a criterion for the restrictions of maximal relations to be continuously invertible and a criterion for the families of these restrictions to be holomorphic are given. The operators inverse to these restrictions are stated to be integral operators. By using the results obtained, the existence of the characteristic operator on the finite interval and the axis is proved. 2011 Article On Linear Relations Generated by a DiRerential Expression and by a Nevanlinna Operator Function / V.M. Bruk // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 2. — С. 115-140. — Бібліогр.: 25 назв. — англ. 1812-9471 http://dspace.nbuv.gov.ua/handle/123456789/106668 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 |
The families of maximal and minimal relations generated by a differential expression with bounded operator coe±cients and by a Nevanlinna operator function are defined. These families are proved to be holomorphic. In the case of finite interval, the space of boundary values is constructed. In terms of boundary conditions, a criterion for the restrictions of maximal relations to be continuously invertible and a criterion for the families of these restrictions to be holomorphic are given. The operators inverse to these restrictions are stated to be integral operators. By using the results obtained, the existence of the characteristic operator on the finite interval and the axis is proved. |
| format |
Article |
| author |
Bruk, V.M. |
| spellingShingle |
Bruk, V.M. On Linear Relations Generated by a DiRerential Expression and by a Nevanlinna Operator Function Журнал математической физики, анализа, геометрии |
| author_facet |
Bruk, V.M. |
| author_sort |
Bruk, V.M. |
| title |
On Linear Relations Generated by a DiRerential Expression and by a Nevanlinna Operator Function |
| title_short |
On Linear Relations Generated by a DiRerential Expression and by a Nevanlinna Operator Function |
| title_full |
On Linear Relations Generated by a DiRerential Expression and by a Nevanlinna Operator Function |
| title_fullStr |
On Linear Relations Generated by a DiRerential Expression and by a Nevanlinna Operator Function |
| title_full_unstemmed |
On Linear Relations Generated by a DiRerential Expression and by a Nevanlinna Operator Function |
| title_sort |
on linear relations generated by a direrential expression and by a nevanlinna operator function |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106668 |
| citation_txt |
On Linear Relations Generated by a DiRerential Expression and by a Nevanlinna Operator Function / V.M. Bruk // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 2. — С. 115-140. — Бібліогр.: 25 назв. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
| work_keys_str_mv |
AT brukvm onlinearrelationsgeneratedbyadirerentialexpressionandbyanevanlinnaoperatorfunction |
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2023-10-18T20:13:26Z |
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2023-10-18T20:13:26Z |
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1796149297822040064 |