Dimeters in $L_2$ classes of differentiated functions determined by continuity moduli of higher orders
Sharp inequalities are obtained in the space $L_2$, connecting the best approximations of differentiable $2\pi$-periodic functions by trigonometric polynomials with integrals containing the higher-order moduli of continuity of the derivatives of these functions. The Kolmogorov widths of certain clas...
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| Datum: | 1991 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1991
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9317 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513495492067328 |
|---|---|
| author | Shalaev , V. V. Шалаев , В. В. |
| author_facet | Shalaev , V. V. Шалаев , В. В. |
| author_sort | Shalaev , V. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-06-19T08:20:09Z |
| description | Sharp inequalities are obtained in the space $L_2$, connecting the best approximations of differentiable $2\pi$-periodic functions by trigonometric polynomials with integrals containing the higher-order moduli of continuity of the derivatives of these functions. The Kolmogorov widths of certain classes of functions, defined by these moduli of continuity, are computed. |
| first_indexed | 2026-03-24T03:45:35Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-9317 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:45:35Z |
| publishDate | 1991 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/6e/dcbdc62684967caa2fb0667b1c8c1c6e |
| spelling | umjimathkievua-article-93172025-06-19T08:20:09Z Dimeters in $L_2$ classes of differentiated functions determined by continuity moduli of higher orders О поперечниках в $L_2$ классов дифференцируемых функций, определяемых модулями непрерывности высших порядков Shalaev , V. V. Шалаев , В. В. Sharp inequalities are obtained in the space $L_2$, connecting the best approximations of differentiable $2\pi$-periodic functions by trigonometric polynomials with integrals containing the higher-order moduli of continuity of the derivatives of these functions. The Kolmogorov widths of certain classes of functions, defined by these moduli of continuity, are computed. В метрике пространства $L_2$ получены точные неравенства, которые связывают наилучшие приближения дифференцируемых $2\pi$-периодических функций тригонометрическими полиномами с интегралами, содержащими модули непрерывности высших порядков производных этих функций. Вычислены поперечники по Колмогорову некоторых классов функций, определяемых этими модулями непрерывности. У метриці простору $L_2$ одержані точні нерівності, які зв’язують найкращі наближення диференційовних $2\pi$-періодичних функцій тригонометричними поліномами з інтегралами, що містять модулі неперервності вищих порядків похідних цих функцій. Обчислені поперечники по Колмогорову деяких класів функцій, що визначаються цими модулями неперервності. Institute of Mathematics, NAS of Ukraine 1991-01-18 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/9317 Ukrains’kyi Matematychnyi Zhurnal; Vol. 43 No. 1 (1991); 125-129 Український математичний журнал; Том 43 № 1 (1991); 125-129 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/9317/10492 Copyright (c) 1991 В. В. Шалаев |
| spellingShingle | Shalaev , V. V. Шалаев , В. В. Dimeters in $L_2$ classes of differentiated functions determined by continuity moduli of higher orders |
| title | Dimeters in $L_2$ classes of differentiated functions determined by continuity moduli of higher orders |
| title_alt | О поперечниках в $L_2$ классов дифференцируемых функций, определяемых модулями непрерывности высших порядков |
| title_full | Dimeters in $L_2$ classes of differentiated functions determined by continuity moduli of higher orders |
| title_fullStr | Dimeters in $L_2$ classes of differentiated functions determined by continuity moduli of higher orders |
| title_full_unstemmed | Dimeters in $L_2$ classes of differentiated functions determined by continuity moduli of higher orders |
| title_short | Dimeters in $L_2$ classes of differentiated functions determined by continuity moduli of higher orders |
| title_sort | dimeters in $l_2$ classes of differentiated functions determined by continuity moduli of higher orders |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9317 |
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