Estimates of the Kolmogorov widths for classes of infinitely differentiable periodic functions
Lower estimates of the Kolmogorov widths are obtained for certain classes of infinitely differentiable periodic functions in the metrics of C and L. For many important cases, these estimates coincide with the values of the best approximations of convolution classes by trigonometric polynomials calcu...
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| Date: | 1997 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1997
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5176 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511379153223680 |
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| author | Serdyuk, A. S. Сердюк, А. С. |
| author_facet | Serdyuk, A. S. Сердюк, А. С. |
| author_sort | Serdyuk, A. S. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:26:15Z |
| description | Lower estimates of the Kolmogorov widths are obtained for certain classes of infinitely differentiable periodic functions in the metrics of C and L. For many important cases, these estimates coincide with the values of the best approximations of convolution classes by trigonometric polynomials calculated by Nagy, and, hence, they are exact. |
| first_indexed | 2026-03-24T03:11:57Z |
| format | Article |
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| id | umjimathkievua-article-5176 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:11:57Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/d9/96882a0d52156a0aa3339034faba58d9.pdf |
| spelling | umjimathkievua-article-51762020-03-18T21:26:15Z Estimates of the Kolmogorov widths for classes of infinitely differentiable periodic functions Оцінки поперечників за Колмогоровим класів нескінченно-диференційовних періодичних функцій Serdyuk, A. S. Сердюк, А. С. Lower estimates of the Kolmogorov widths are obtained for certain classes of infinitely differentiable periodic functions in the metrics of C and L. For many important cases, these estimates coincide with the values of the best approximations of convolution classes by trigonometric polynomials calculated by Nagy, and, hence, they are exact. Одержано оцінки знизу поперечників за Колмогоровим деяких класів нескінченно-диферен-ційовних періодичних функцій у метриках C і L. В ряді важливих випадків ці оцінки збігаються з величинами найкращих наближень класів згорток тригонометричними поліномами, обчисленими Б. Надем і, отже, виявляються точними. Institute of Mathematics, NAS of Ukraine 1997-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5176 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 12 (1997); 1700–1706 Український математичний журнал; Том 49 № 12 (1997); 1700–1706 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5176/7048 https://umj.imath.kiev.ua/index.php/umj/article/view/5176/7049 Copyright (c) 1997 Serdyuk A. S. |
| spellingShingle | Serdyuk, A. S. Сердюк, А. С. Estimates of the Kolmogorov widths for classes of infinitely differentiable periodic functions |
| title | Estimates of the Kolmogorov widths for classes of infinitely differentiable periodic functions |
| title_alt | Оцінки поперечників за Колмогоровим класів нескінченно-диференційовних періодичних функцій |
| title_full | Estimates of the Kolmogorov widths for classes of infinitely differentiable periodic functions |
| title_fullStr | Estimates of the Kolmogorov widths for classes of infinitely differentiable periodic functions |
| title_full_unstemmed | Estimates of the Kolmogorov widths for classes of infinitely differentiable periodic functions |
| title_short | Estimates of the Kolmogorov widths for classes of infinitely differentiable periodic functions |
| title_sort | estimates of the kolmogorov widths for classes of infinitely differentiable periodic functions |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5176 |
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