Characteristic functions of almost soluble expansion of the Hermitian operators
The characteristic operator-functions W(λ) are studied of the almost solvable extensions of an Hermitian operator. The inverse problem is solved, a multiplication theorem is proved, and a formula is derived expressing W(λ) in terms of the Weyl function and the boundary operator. Characteristic funct...
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| Date: | 1992 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian |
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Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7885 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512800283033600 |
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| author | Derkach , V. A. Malamud , M. M. Деркач , В. А. Маламуд , М. М. |
| author_facet | Derkach , V. A. Malamud , M. M. Деркач , В. А. Маламуд , М. М. |
| author_sort | Derkach , V. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-10-26T11:41:49Z |
| description | The characteristic operator-functions W(λ) are studied of the almost solvable extensions of an Hermitian operator. The inverse problem is solved, a multiplication theorem is proved, and a formula is derived expressing W(λ) in terms of the Weyl function and the boundary operator. Characteristic functions are computed of various differential and difference operators, with the help of which are proved theorems of the completeness of the systems of proper and adjoint vectors. |
| first_indexed | 2026-03-24T03:34:32Z |
| format | Article |
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| id | umjimathkievua-article-7885 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:34:32Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/65/21cc0ed82d0763e18fd897f489061065.pdf |
| spelling | umjimathkievua-article-78852023-10-26T11:41:49Z Characteristic functions of almost soluble expansion of the Hermitian operators Характеристические функции почти разрешимых расширений эрмитовых операторов Derkach , V. A. Malamud , M. M. Деркач , В. А. Маламуд , М. М. The characteristic operator-functions W(λ) are studied of the almost solvable extensions of an Hermitian operator. The inverse problem is solved, a multiplication theorem is proved, and a formula is derived expressing W(λ) in terms of the Weyl function and the boundary operator. Characteristic functions are computed of various differential and difference operators, with the help of which are proved theorems of the completeness of the systems of proper and adjoint vectors. Изучаются характеристические оператор-функции W(λ) почти разрешимых расширений эрмитова оператора. Решена обратная задача, доказана теорема умножения, выведена ормула, выражающая W(λ) через функцию Вейля и граничный оператор. Вычислены характеристические функции различных дифференциальных и разностных операторов, с помощью которых доказаны теоремы полноты систем собственных и присоединенных векторов. Вивчаються характеристичні оператор-функції W(λ) майже розв’язних розширень ермітова оператора. Розв’язана обернена задача, доведена теорема множення, виведена формула, яка виражає W (λ) через функцію Вейля і крайовий оператор. Обчислені характеристичні функції різних диференціальних і різницевих операторів, за допомогою яких доведені теореми повноти системи власних та приєднаних векторів. Institute of Mathematics, NAS of Ukraine 1992-04-17 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7885 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 4 (1992); 435-459 Український математичний журнал; Том 44 № 4 (1992); 435-459 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/7885/9505 Copyright (c) 1992 V. A. Derkach , M. M. Malamud |
| spellingShingle | Derkach , V. A. Malamud , M. M. Деркач , В. А. Маламуд , М. М. Characteristic functions of almost soluble expansion of the Hermitian operators |
| title | Characteristic functions of almost soluble expansion of the Hermitian operators |
| title_alt | Характеристические функции почти разрешимых расширений эрмитовых операторов |
| title_full | Characteristic functions of almost soluble expansion of the Hermitian operators |
| title_fullStr | Characteristic functions of almost soluble expansion of the Hermitian operators |
| title_full_unstemmed | Characteristic functions of almost soluble expansion of the Hermitian operators |
| title_short | Characteristic functions of almost soluble expansion of the Hermitian operators |
| title_sort | characteristic functions of almost soluble expansion of the hermitian operators |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7885 |
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