Approximation of classes of periodic functions with small smoothness
We prove that the approximations of classes of periodic functions with small smoothness in the metrics of the spaces C and L by different linear summation methods for Fourier series are asymptotically equal to the least upper bounds of the best approximations of these classes by trigonometric polyno...
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| Date: | 2000 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2000
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4407 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510536962146304 |
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| author | Bushev, D. M. Бушев, Д. М. |
| author_facet | Bushev, D. M. Бушев, Д. М. |
| author_sort | Bushev, D. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:28:32Z |
| description | We prove that the approximations of classes of periodic functions with small smoothness in the metrics of the spaces C and L by different linear summation methods for Fourier series are asymptotically equal to the least upper bounds of the best approximations of these classes by trigonometric polynomials of degree not higher than (n - 1). We establish that the Fejér method is asymptotically the best among all positive linear approximation methods for these classes. |
| first_indexed | 2026-03-24T02:58:34Z |
| format | Article |
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| id | umjimathkievua-article-4407 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:58:34Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/fb/3bbaf5fc9fa6d34fc567248c10f7d2fb.pdf |
| spelling | umjimathkievua-article-44072020-03-18T20:28:32Z Approximation of classes of periodic functions with small smoothness Наближення класів періодичних функцій з невеликою гладкістю Bushev, D. M. Бушев, Д. М. We prove that the approximations of classes of periodic functions with small smoothness in the metrics of the spaces C and L by different linear summation methods for Fourier series are asymptotically equal to the least upper bounds of the best approximations of these classes by trigonometric polynomials of degree not higher than (n - 1). We establish that the Fejér method is asymptotically the best among all positive linear approximation methods for these classes. Доведено, що наближення класів періодичних функцій з невеликою гладкістю в метриках просторів $С$ і $L$ різними лінійними методами підсумовування рядів Фур'є асимптотично рівні точним верхнім межам найкращих наближень цих класів тригонометричними поліномами степеня, що не перевищує $(n - 1)$. Встановлено, що метод Фейєра є асимптотично найкращим серед усіх додатних лінійних методів наближення цих класів. Institute of Mathematics, NAS of Ukraine 2000-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4407 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 2 (2000); 183-196 Український математичний журнал; Том 52 № 2 (2000); 183-196 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4407/5518 https://umj.imath.kiev.ua/index.php/umj/article/view/4407/5519 Copyright (c) 2000 Bushev D. M. |
| spellingShingle | Bushev, D. M. Бушев, Д. М. Approximation of classes of periodic functions with small smoothness |
| title | Approximation of classes of periodic functions with small smoothness |
| title_alt | Наближення класів періодичних функцій з невеликою гладкістю |
| title_full | Approximation of classes of periodic functions with small smoothness |
| title_fullStr | Approximation of classes of periodic functions with small smoothness |
| title_full_unstemmed | Approximation of classes of periodic functions with small smoothness |
| title_short | Approximation of classes of periodic functions with small smoothness |
| title_sort | approximation of classes of periodic functions with small smoothness |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4407 |
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