Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials
We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the classes of periodic infinitely differentiable functions C Ψ β C whose elements can be represented in the form of convolutions with fixed generating kernels. We obtain asymptotic equalities for upper...
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| Date: | 2004 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2004
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3771 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509903236366336 |
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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 | 2020-03-18T20:08:07Z |
| description | We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the classes of periodic infinitely differentiable functions C Ψ β C whose elements can be represented in the form of convolutions with fixed generating kernels. We obtain asymptotic equalities for upper bounds of approximations by interpolation trigonometric polynomials on the classes C Ψ β,∞ and C Ψ β H ω. |
| first_indexed | 2026-03-24T02:48:30Z |
| format | Article |
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| id | umjimathkievua-article-3771 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:48:30Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/ae/1d3e201145a4548f97c09585adf021ae.pdf |
| spelling | umjimathkievua-article-37712020-03-18T20:08:07Z Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials Наближення нескінченно диференційовних періодичних функцій інтерполяційними тригонометричними поліномами Serdyuk, A. S. Сердюк, А. С. We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the classes of periodic infinitely differentiable functions C Ψ β C whose elements can be represented in the form of convolutions with fixed generating kernels. We obtain asymptotic equalities for upper bounds of approximations by interpolation trigonometric polynomials on the classes C Ψ β,∞ and C Ψ β H ω. Встановлено асимптотично непокращуваиі інтерполяційні аналоги нерівностей типу Лебега на класах періодичних нескінченно диферепційовімх функцій C Ψ β C, елементи яких допускають зображення у вигляді згорток із фіксованими твірними ядрами. Знайдено асимптотичні рівності для верхніх меж наближень інтерполяційними тригонометричними поліномами на класах C Ψ β,∞ and C Ψ β H ω. Institute of Mathematics, NAS of Ukraine 2004-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3771 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 4 (2004); 495–505 Український математичний журнал; Том 56 № 4 (2004); 495–505 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/3771/4264 https://umj.imath.kiev.ua/index.php/umj/article/view/3771/4265 Copyright (c) 2004 Serdyuk A. S. |
| spellingShingle | Serdyuk, A. S. Сердюк, А. С. Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials |
| title | Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials |
| title_alt | Наближення нескінченно диференційовних періодичних функцій інтерполяційними тригонометричними поліномами |
| title_full | Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials |
| title_fullStr | Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials |
| title_full_unstemmed | Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials |
| title_short | Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials |
| title_sort | approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3771 |
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