Approximation of classes of analytic functions by algebraic polynomials and kolmogorov widths
We obtain estimates of the best polynomial approximations, uniform in the closure $B$ of Faber domains of the complex plane $ℂ$, for functions continuous in $B$ and defined by Cauchy-type integrals with densities possessing certain generalized differential properties. We establish estimates exact in...
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| Date: | 1996 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1996
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5351 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511579680800768 |
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| author | Romanyuk, V. S. Романюк, В. С. Романюк, В. С. |
| author_facet | Romanyuk, V. S. Романюк, В. С. Романюк, В. С. |
| author_sort | Romanyuk, V. S. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:30:56Z |
| description | We obtain estimates of the best polynomial approximations, uniform in the closure $B$ of Faber domains of the complex plane $ℂ$, for functions continuous in $B$ and defined by Cauchy-type integrals with densities possessing certain generalized differential properties. We establish estimates exact in order for the Kolmogorov widths of classes of such functions in relevant functional spaces. |
| first_indexed | 2026-03-24T03:15:08Z |
| format | Article |
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| id | umjimathkievua-article-5351 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:15:08Z |
| publishDate | 1996 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/6a/26acb8925be3629d7e3397cb6ec29e6a.pdf |
| spelling | umjimathkievua-article-53512020-03-18T21:30:56Z Approximation of classes of analytic functions by algebraic polynomials and kolmogorov widths Приближение классов аналитических функций алгебраическими многочленами и колмогоровские поперечники Romanyuk, V. S. Романюк, В. С. Романюк, В. С. We obtain estimates of the best polynomial approximations, uniform in the closure $B$ of Faber domains of the complex plane $ℂ$, for functions continuous in $B$ and defined by Cauchy-type integrals with densities possessing certain generalized differential properties. We establish estimates exact in order for the Kolmogorov widths of classes of such functions in relevant functional spaces. Знайдені оцінки найкращих рівномірних в замиканні $B$ фаберових областей комплексної площини $ℂ$ поліноміальних наближень неперервних в $B$ функцій, що визначаються інтегралами типу Коші, щільності яких мають певні узагальнені диференціальні властивості. Встановлені точні за порядком оцінки колмогоровських поперечників класів таких функцій у відповідних функціональних просторах. Institute of Mathematics, NAS of Ukraine 1996-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5351 Ukrains’kyi Matematychnyi Zhurnal; Vol. 48 No. 2 (1996); 236-250 Український математичний журнал; Том 48 № 2 (1996); 236-250 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5351/7393 https://umj.imath.kiev.ua/index.php/umj/article/view/5351/7394 Copyright (c) 1996 Romanyuk V. S. |
| spellingShingle | Romanyuk, V. S. Романюк, В. С. Романюк, В. С. Approximation of classes of analytic functions by algebraic polynomials and kolmogorov widths |
| title | Approximation of classes of analytic functions by algebraic polynomials and kolmogorov widths |
| title_alt | Приближение классов аналитических функций алгебраическими многочленами и колмогоровские поперечники |
| title_full | Approximation of classes of analytic functions by algebraic polynomials and kolmogorov widths |
| title_fullStr | Approximation of classes of analytic functions by algebraic polynomials and kolmogorov widths |
| title_full_unstemmed | Approximation of classes of analytic functions by algebraic polynomials and kolmogorov widths |
| title_short | Approximation of classes of analytic functions by algebraic polynomials and kolmogorov widths |
| title_sort | approximation of classes of analytic functions by algebraic polynomials and kolmogorov widths |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5351 |
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