On uniform approximations of almost periodic functions by entire functions of finite degree
We give a new proof of the well-known Bernshtein statement that, among entire functions of degree $≤ σ$ which realize the best uniform approximation (of degree $σ$) of a periodic function on $(−∞,∞)$, there is a trigonometric polynomial of degree $≤ σ$. We prove an analog of the mentioned Bernshtein...
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| Datum: | 1995 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1995
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5528 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511758861467648 |
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| author | Timan, M. F. Тиман, М. Ф. Тиман, М. Ф. |
| author_facet | Timan, M. F. Тиман, М. Ф. Тиман, М. Ф. |
| author_sort | Timan, M. F. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:12:37Z |
| description | We give a new proof of the well-known Bernshtein statement that, among entire functions of degree $≤ σ$ which realize the best uniform approximation (of degree $σ$) of a periodic function on $(−∞,∞)$, there is a trigonometric polynomial of degree $≤ σ$. We prove an analog of the mentioned Bernshtein statement and the Jackson theorem for uniform almost periodic functions with arbitrary spectrum. |
| first_indexed | 2026-03-24T03:17:59Z |
| format | Article |
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| id | umjimathkievua-article-5528 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:17:59Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/f6/1ed44f3791838f62509309cca7544bf6.pdf |
| spelling | umjimathkievua-article-55282020-03-19T09:12:37Z On uniform approximations of almost periodic functions by entire functions of finite degree равномерных приближениях почти периодических функций целыми функциями конечной степени Timan, M. F. Тиман, М. Ф. Тиман, М. Ф. We give a new proof of the well-known Bernshtein statement that, among entire functions of degree $≤ σ$ which realize the best uniform approximation (of degree $σ$) of a periodic function on $(−∞,∞)$, there is a trigonometric polynomial of degree $≤ σ$. We prove an analog of the mentioned Bernshtein statement and the Jackson theorem for uniform almost periodic functions with arbitrary spectrum. Наводиться доведення відомого твердження С. И. Бернштейна про те, що серед цілих функцій степеня $≤ σ$, які на $(−∞,∞)$ найкраще рівномірно наближають (з порядком $σ$) періодичну функцію, існує тригонометричний поліном степеня $≤ σ$. Доведено аналог цього твердження С. И. Бернштейна та теорему Джексона для рівномірних майже періодичних функцій з довільним спектром. Institute of Mathematics, NAS of Ukraine 1995-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5528 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 9 (1995); 1274–1279 Український математичний журнал; Том 47 № 9 (1995); 1274–1279 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5528/7744 https://umj.imath.kiev.ua/index.php/umj/article/view/5528/7745 Copyright (c) 1995 Timan M. F. |
| spellingShingle | Timan, M. F. Тиман, М. Ф. Тиман, М. Ф. On uniform approximations of almost periodic functions by entire functions of finite degree |
| title | On uniform approximations of almost periodic functions by entire functions of finite degree |
| title_alt | равномерных приближениях почти периодических функций целыми
функциями конечной степени |
| title_full | On uniform approximations of almost periodic functions by entire functions of finite degree |
| title_fullStr | On uniform approximations of almost periodic functions by entire functions of finite degree |
| title_full_unstemmed | On uniform approximations of almost periodic functions by entire functions of finite degree |
| title_short | On uniform approximations of almost periodic functions by entire functions of finite degree |
| title_sort | on uniform approximations of almost periodic functions by entire functions of finite degree |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5528 |
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