Approximation of $\bar {\psi} - integrals$−integrals of periodic functions by Fourier sums (small smoothness). Iof periodic functions by Fourier sums (small smoothness). I
We investigate the rate of convergence of Fourier series on the classes $L^{\bar {\psi} } \text{N}$ in the uniform and integral metrics. The results obtained are extended to the case where the classes $L^{\bar {\psi} } \text{N}$ are the classes of convolutions of functions from $\text{N}$ with...
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| Datum: | 1998 |
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Institute of Mathematics, NAS of Ukraine
1998
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511150254325760 |
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| author | Stepanets, O. I. Степанец, А. И. Степанец, А. И. |
| author_facet | Stepanets, O. I. Степанец, А. И. Степанец, А. И. |
| author_sort | Stepanets, O. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:20:56Z |
| description | We investigate the rate of convergence of Fourier series on the classes $L^{\bar {\psi} } \text{N}$ in the uniform and integral metrics. The results obtained are extended to the case where the classes $L^{\bar {\psi} } \text{N}$ are the classes of convolutions of functions from $\text{N}$ with kernels with slowly decreasing coefficients. In particular, we obtain asymptotic equalities for the upper bounds of deviations of the Fourier sums on the sets $L^{\bar {\psi} } \text{N}$ which are solutions of the Kolmogorov-Nikol’skii problem. In addition, we establish an analog of the well-known Lebesgue inequality. |
| first_indexed | 2026-03-24T03:08:19Z |
| format | Article |
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| id | umjimathkievua-article-4961 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:08:19Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b0/4660498550b4d4d72b66dc54b7e815b0.pdf |
| spelling | umjimathkievua-article-49612020-03-18T21:20:56Z Approximation of $\bar {\psi} - integrals$−integrals of periodic functions by Fourier sums (small smoothness). Iof periodic functions by Fourier sums (small smoothness). I Приближение $\bar {\psi}$-интегралов периодических функций суммами Фурье (небольшая гладкость). I Stepanets, O. I. Степанец, А. И. Степанец, А. И. We investigate the rate of convergence of Fourier series on the classes $L^{\bar {\psi} } \text{N}$ in the uniform and integral metrics. The results obtained are extended to the case where the classes $L^{\bar {\psi} } \text{N}$ are the classes of convolutions of functions from $\text{N}$ with kernels with slowly decreasing coefficients. In particular, we obtain asymptotic equalities for the upper bounds of deviations of the Fourier sums on the sets $L^{\bar {\psi} } \text{N}$ which are solutions of the Kolmogorov-Nikol’skii problem. In addition, we establish an analog of the well-known Lebesgue inequality. Вивчається швидкість збіжності рядів Фур'є на класах $L^{\bar {\psi} } \text{N}$ в рівномірній та інтегральній метриках. Результати роботи поширюються на випадок, коли класи $L^{\bar {\psi} } \text{N}$ є класами згорток функцій із $\text{N}$ з ядрами, коефіцієнти яких є повільно спадними. В цьому напрямі, зокрема, одержані асимптотичні рівності для верхніх меж відхилень сум Фур'є на множинах $L^{\bar {\psi} } \text{N}$ які є розв'язками задачі Колмогорова - Нікольського, а також знайдено аналог відомої нерівності Лебега. Institute of Mathematics, NAS of Ukraine 1998-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4961 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 2 (1998); 274-291 Український математичний журнал; Том 50 № 2 (1998); 274-291 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4961/6621 https://umj.imath.kiev.ua/index.php/umj/article/view/4961/6622 Copyright (c) 1998 Stepanets O. I. |
| spellingShingle | Stepanets, O. I. Степанец, А. И. Степанец, А. И. Approximation of $\bar {\psi} - integrals$−integrals of periodic functions by Fourier sums (small smoothness). Iof periodic functions by Fourier sums (small smoothness). I |
| title | Approximation of $\bar {\psi} - integrals$−integrals of periodic functions by Fourier sums (small smoothness). Iof periodic functions by Fourier sums (small smoothness). I |
| title_alt | Приближение $\bar {\psi}$-интегралов периодических функций суммами Фурье (небольшая гладкость). I |
| title_full | Approximation of $\bar {\psi} - integrals$−integrals of periodic functions by Fourier sums (small smoothness). Iof periodic functions by Fourier sums (small smoothness). I |
| title_fullStr | Approximation of $\bar {\psi} - integrals$−integrals of periodic functions by Fourier sums (small smoothness). Iof periodic functions by Fourier sums (small smoothness). I |
| title_full_unstemmed | Approximation of $\bar {\psi} - integrals$−integrals of periodic functions by Fourier sums (small smoothness). Iof periodic functions by Fourier sums (small smoothness). I |
| title_short | Approximation of $\bar {\psi} - integrals$−integrals of periodic functions by Fourier sums (small smoothness). Iof periodic functions by Fourier sums (small smoothness). I |
| title_sort | approximation of $\bar {\psi} - integrals$−integrals of periodic functions by fourier sums (small smoothness). iof periodic functions by fourier sums (small smoothness). i |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4961 |
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