On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the InЇnite-Dimensional Case
We define the families of maximal and minimal relations generated by an integral equation with a Nevanlinna operator measure in the infinite-dimensional case and prove their holomorphic property. We show that if the restrictions of maximal relations are continuously invertible, then the operators in...
Збережено в:
| Дата: | 2014 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2014
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/106790 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the InЇnite-Dimensional Case / V.M. Bruk // Журнал математической физики, анализа, геометрии. — 2014. — Т. 10, № 2. — С. 163-188. — Бібліогр.: 24 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-106790 |
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irk-123456789-1067902016-10-06T03:02:11Z On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the InЇnite-Dimensional Case Bruk, V.M. We define the families of maximal and minimal relations generated by an integral equation with a Nevanlinna operator measure in the infinite-dimensional case and prove their holomorphic property. We show that if the restrictions of maximal relations are continuously invertible, then the operators inverse to these restrictions are integral. By using these results, we prove the existence of the characteristic operator and describe the families of linear relations generating the characteristic operator. Определено семейства максимальных и минимальных отношений, порожденных интегральным уравнением с неванлинновской операторной мерой в бесконечномерном случае и доказано, что эти семейства голоморфны. Показано, что если сужения максимальных отношений непрерывно обратимы, то операторы, обратные к таким сужениям, являются интегральными. Используя эти результаты, доказываем существование характеристического оператора и описываем семейства линейных отношений, порождающих характеристический оператор. 2014 Article On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the InЇnite-Dimensional Case / V.M. Bruk // Журнал математической физики, анализа, геометрии. — 2014. — Т. 10, № 2. — С. 163-188. — Бібліогр.: 24 назв. — англ. 1812-9471 http://dspace.nbuv.gov.ua/handle/123456789/106790 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 |
We define the families of maximal and minimal relations generated by an integral equation with a Nevanlinna operator measure in the infinite-dimensional case and prove their holomorphic property. We show that if the restrictions of maximal relations are continuously invertible, then the operators inverse to these restrictions are integral. By using these results, we prove the existence of the characteristic operator and describe the families of linear relations generating the characteristic operator. |
| format |
Article |
| author |
Bruk, V.M. |
| spellingShingle |
Bruk, V.M. On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the InЇnite-Dimensional Case Журнал математической физики, анализа, геометрии |
| author_facet |
Bruk, V.M. |
| author_sort |
Bruk, V.M. |
| title |
On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the InЇnite-Dimensional Case |
| title_short |
On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the InЇnite-Dimensional Case |
| title_full |
On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the InЇnite-Dimensional Case |
| title_fullStr |
On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the InЇnite-Dimensional Case |
| title_full_unstemmed |
On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the InЇnite-Dimensional Case |
| title_sort |
on the characteristic operator of an integral equation with a nevanlinna measure in the inїnite-dimensional case |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106790 |
| citation_txt |
On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the InЇnite-Dimensional Case / V.M. Bruk // Журнал математической физики, анализа, геометрии. — 2014. — Т. 10, № 2. — С. 163-188. — Бібліогр.: 24 назв. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
| work_keys_str_mv |
AT brukvm onthecharacteristicoperatorofanintegralequationwithanevanlinnameasureintheinínitedimensionalcase |
| first_indexed |
2023-10-18T20:13:42Z |
| last_indexed |
2023-10-18T20:13:42Z |
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1796149309094232064 |