On manifolds of eigenfunctions and potentials generated by a family of periodic boundary-value problems
We consider a family of boundary-value problems with some potential as a parameter. We study the manifold of normalized eigenfunctions with even number of zeros in a period, and the manifold of potentials associated with double eigenvalues. In particular, we prove that the manifold of normalized eig...
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| Date: | 1996 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1996
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5277 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511492421451776 |
|---|---|
| author | Dymarskii, Ya. M. Дымарский, Я. М. Дымарский, Я. М. |
| author_facet | Dymarskii, Ya. M. Дымарский, Я. М. Дымарский, Я. М. |
| author_sort | Dymarskii, Ya. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:29:27Z |
| description | We consider a family of boundary-value problems with some potential as a parameter. We study the manifold of normalized eigenfunctions with even number of zeros in a period, and the manifold of potentials associated with double eigenvalues. In particular, we prove that the manifold of normalized eigenfunctions is a trivial fiber space over a unit circle and that the manifold of potentials with double eigenvalues is a homotopically trivial manifold trivially imbedded into the space of potentials. |
| first_indexed | 2026-03-24T03:13:45Z |
| format | Article |
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| id | umjimathkievua-article-5277 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:13:45Z |
| publishDate | 1996 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/4d/a734403eaa0b85a2d699633cd25da44d.pdf |
| spelling | umjimathkievua-article-52772020-03-18T21:29:27Z On manifolds of eigenfunctions and potentials generated by a family of periodic boundary-value problems О многообразиях собственных функций и потенциалов, порожденных семейством периодических краевых задач Dymarskii, Ya. M. Дымарский, Я. М. Дымарский, Я. М. We consider a family of boundary-value problems with some potential as a parameter. We study the manifold of normalized eigenfunctions with even number of zeros in a period, and the manifold of potentials associated with double eigenvalues. In particular, we prove that the manifold of normalized eigenfunctions is a trivial fiber space over a unit circle and that the manifold of potentials with double eigenvalues is a homotopically trivial manifold trivially imbedded into the space of potentials. Розглянуто сукупність крайових задач, в яких параметром е деякий потенціал. Досліджено миоговид нормованих власних функцій, що мають на періоді парну кількість нулів, та многовид потенціалів, яким відповідають двократні власні значення. Доведено, зокрема, що многовид нормованих власних функцій е тривіально розшарованим простором над одиничним колом, а многовид потенціалів з двократними власними значеннями є гомотопно тривіальним многовидом, тривіально вкладеним у простір потенціалів. Institute of Mathematics, NAS of Ukraine 1996-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5277 Ukrains’kyi Matematychnyi Zhurnal; Vol. 48 No. 6 (1996); 771-781 Український математичний журнал; Том 48 № 6 (1996); 771-781 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5277/7246 https://umj.imath.kiev.ua/index.php/umj/article/view/5277/7247 Copyright (c) 1996 Dymarskii Ya. M. |
| spellingShingle | Dymarskii, Ya. M. Дымарский, Я. М. Дымарский, Я. М. On manifolds of eigenfunctions and potentials generated by a family of periodic boundary-value problems |
| title | On manifolds of eigenfunctions and potentials generated by a family of periodic boundary-value problems |
| title_alt | О многообразиях собственных функций и потенциалов, порожденных семейством периодических краевых задач |
| title_full | On manifolds of eigenfunctions and potentials generated by a family of periodic boundary-value problems |
| title_fullStr | On manifolds of eigenfunctions and potentials generated by a family of periodic boundary-value problems |
| title_full_unstemmed | On manifolds of eigenfunctions and potentials generated by a family of periodic boundary-value problems |
| title_short | On manifolds of eigenfunctions and potentials generated by a family of periodic boundary-value problems |
| title_sort | on manifolds of eigenfunctions and potentials generated by a family of periodic boundary-value problems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5277 |
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