Approximation of $\bar {\psi} - \text{Integrals}$ of periodic functions by Fourier sums (small smoothness). IIof periodic functions by Fourier sums (small smoothness). II
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 $\text{N}$ wi...
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| Datum: | 1998 |
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Institute of Mathematics, NAS of Ukraine
1998
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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 | 2020-03-18T21:17:35Z |
| 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 | 2026-03-24T03:07:54Z |
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| id | umjimathkievua-article-4938 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
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| language | rus English |
| last_indexed | 2026-03-24T03:07:54Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
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| resource_txt_mv | umjimathkievua/07/adf649558fe353a5b1553bf1c63a7407.pdf |
| spelling | umjimathkievua-article-49382020-03-18T21:17:35Z Approximation of $\bar {\psi} - \text{Integrals}$ of periodic functions by Fourier sums (small smoothness). IIof periodic functions by Fourier sums (small smoothness). II Приближение $\bar {\psi}$-интегралов периодических функций суммами Фурье (небольшая гладкость). II 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. Продовжується вивчення швидкості 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 1998-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4938 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 3 (1998); 388-400 Український математичний журнал; Том 50 № 3 (1998); 388-400 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4938/6575 https://umj.imath.kiev.ua/index.php/umj/article/view/4938/6576 Copyright (c) 1998 Stepanets O. I. |
| spellingShingle | Stepanets, O. I. Степанец, А. И. Степанец, А. И. Approximation of $\bar {\psi} - \text{Integrals}$ of periodic functions by Fourier sums (small smoothness). IIof periodic functions by Fourier sums (small smoothness). II |
| title | Approximation of $\bar {\psi} - \text{Integrals}$ of periodic functions by Fourier sums (small smoothness). IIof periodic functions by Fourier sums (small smoothness). II |
| title_alt | Приближение $\bar {\psi}$-интегралов периодических функций суммами Фурье (небольшая гладкость). II
|
| title_full | Approximation of $\bar {\psi} - \text{Integrals}$ of periodic functions by Fourier sums (small smoothness). IIof periodic functions by Fourier sums (small smoothness). II |
| title_fullStr | Approximation of $\bar {\psi} - \text{Integrals}$ of periodic functions by Fourier sums (small smoothness). IIof periodic functions by Fourier sums (small smoothness). II |
| title_full_unstemmed | Approximation of $\bar {\psi} - \text{Integrals}$ of periodic functions by Fourier sums (small smoothness). IIof periodic functions by Fourier sums (small smoothness). II |
| title_short | Approximation of $\bar {\psi} - \text{Integrals}$ of periodic functions by Fourier sums (small smoothness). IIof periodic functions by Fourier sums (small smoothness). II |
| title_sort | approximation of $\bar {\psi} - \text{integrals}$ of periodic functions by fourier sums (small smoothness). iiof periodic functions by fourier sums (small smoothness). ii |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4938 |
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