Singularly perturbed normal operators
We present a generalization of definition'of-singularly perturbed operators to the case of normal operators. To do this, we use an idea of normal expansions of a prenormal operator and prove the relation for resolvents of normal expansions similar to the M. Krein relation for resolvents of...
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| Datum: | 1999 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1999
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4695 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510859687624704 |
|---|---|
| author | Dudkin, M. Ye. Дудкін, М. Є. |
| author_facet | Dudkin, M. Ye. Дудкін, М. Є. |
| author_sort | Dudkin, M. Ye. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:11:43Z |
| description | We present a generalization of definition'of-singularly perturbed operators to the case of normal operators. To do this, we use an idea of normal expansions of a prenormal operator and prove the relation for resolvents of normal expansions similar to the M. Krein relation for resolvents of self-adjoint expansions. In addition, we establish one-to-one correspondence between the set of singular perturbations of rank one and the set of perturbed (of rank one) operators. |
| first_indexed | 2026-03-24T03:03:42Z |
| format | Article |
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| id | umjimathkievua-article-4695 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:03:42Z |
| publishDate | 1999 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/64/cfcf3699e20a82eb527fa3dbbbb8d164.pdf |
| spelling | umjimathkievua-article-46952020-03-18T21:11:43Z Singularly perturbed normal operators Сингулярно збурені нормальні оператори Dudkin, M. Ye. Дудкін, М. Є. We present a generalization of definition'of-singularly perturbed operators to the case of normal operators. To do this, we use an idea of normal expansions of a prenormal operator and prove the relation for resolvents of normal expansions similar to the M. Krein relation for resolvents of self-adjoint expansions. In addition, we establish one-to-one correspondence between the set of singular perturbations of rank one and the set of perturbed (of rank one) operators. Наведено узагальнення означення сингулярно збурених операторів на випадок нормальних операторів. Для цього використано ідею нормальних розширень передиормального оператора і доведено формулу для резольвент нормальних розширень типу М. Г. Крейиа для резольвент само-спряжеиих розширень. Крім цього встановлено взаємно однозначну відповідність між множиною сингулярних збурень рангу один і множиною сингулярно збурених (рангу один) операторів. Institute of Mathematics, NAS of Ukraine 1999-08-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4695 Ukrains’kyi Matematychnyi Zhurnal; Vol. 51 No. 8 (1999); 1045–1053 Український математичний журнал; Том 51 № 8 (1999); 1045–1053 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4695/6092 https://umj.imath.kiev.ua/index.php/umj/article/view/4695/6093 Copyright (c) 1999 Dudkin M. Ye. |
| spellingShingle | Dudkin, M. Ye. Дудкін, М. Є. Singularly perturbed normal operators |
| title | Singularly perturbed normal operators |
| title_alt | Сингулярно збурені нормальні оператори |
| title_full | Singularly perturbed normal operators |
| title_fullStr | Singularly perturbed normal operators |
| title_full_unstemmed | Singularly perturbed normal operators |
| title_short | Singularly perturbed normal operators |
| title_sort | singularly perturbed normal operators |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4695 |
| work_keys_str_mv | AT dudkinmye singularlyperturbednormaloperators AT dudkínmê singularlyperturbednormaloperators AT dudkinmye singulârnozburenínormalʹníoperatori AT dudkínmê singulârnozburenínormalʹníoperatori |