An example of a complete orthonormal system in a Hilbert space of generalized functions
We construct a complete orthonormal system of generalized functions in a Hilbert space W −1. We obtain an estimate of the error of approximation in W −1, which is expressed in terms of the integral modulus of continuity of a function from L 2.
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| Datum: | 1997 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1997
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5055 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511248001531904 |
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| author | Gladkivs’ka, O. V. Гладківська, О. В. |
| author_facet | Gladkivs’ka, O. V. Гладківська, О. В. |
| author_sort | Gladkivs’ka, O. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:23:40Z |
| description | We construct a complete orthonormal system of generalized functions in a Hilbert space W −1. We obtain an estimate of the error of approximation in W −1, which is expressed in terms of the integral modulus of continuity of a function from L 2. |
| first_indexed | 2026-03-24T03:09:52Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5055 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:09:52Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/a1/56b52395ab77492852a6ee7f53086fa1.pdf |
| spelling | umjimathkievua-article-50552020-03-18T21:23:40Z An example of a complete orthonormal system in a Hilbert space of generalized functions Приклад повної ортопормованої системи в гільбертовому просторі узагальнених функцій Gladkivs’ka, O. V. Гладківська, О. В. We construct a complete orthonormal system of generalized functions in a Hilbert space W −1. We obtain an estimate of the error of approximation in W −1, which is expressed in terms of the integral modulus of continuity of a function from L 2. Побудовано повну ортонормовану систему узагальнених функцій у гільбертовому просторі W −1. Знайдено оцінку похибки апроксимації в W −1, яка виражається через інтегральний модуль неперервності функції з L 2. Institute of Mathematics, NAS of Ukraine 1997-05-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5055 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 5 (1997); 725–728 Український математичний журнал; Том 49 № 5 (1997); 725–728 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5055/6807 https://umj.imath.kiev.ua/index.php/umj/article/view/5055/6808 Copyright (c) 1997 Gladkivs’ka O. V. |
| spellingShingle | Gladkivs’ka, O. V. Гладківська, О. В. An example of a complete orthonormal system in a Hilbert space of generalized functions |
| title | An example of a complete orthonormal system in a Hilbert space of generalized functions |
| title_alt | Приклад повної ортопормованої системи в гільбертовому просторі узагальнених функцій |
| title_full | An example of a complete orthonormal system in a Hilbert space of generalized functions |
| title_fullStr | An example of a complete orthonormal system in a Hilbert space of generalized functions |
| title_full_unstemmed | An example of a complete orthonormal system in a Hilbert space of generalized functions |
| title_short | An example of a complete orthonormal system in a Hilbert space of generalized functions |
| title_sort | example of a complete orthonormal system in a hilbert space of generalized functions |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5055 |
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