Approximation of cauchy-type integrals in Jordan domains
The concept of a generalized ψ-derivative of a function of a complex variable is introduced and applied to classify functions analytic in Jordan domains. The approximations of functions from the classes introduced by this procedure are studied by using algebraic polynomials constructed on the basis...
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| Datum: | 1993 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1993
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5870 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512091435171840 |
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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 | 2020-03-19T09:19:41Z |
| description | The concept of a generalized ψ-derivative of a function of a complex variable is introduced and applied to classify functions analytic in Jordan domains. The approximations of functions from the classes introduced by this procedure are studied by using algebraic polynomials constructed on the basis of the Faber polynomials after the summation of Faber series. Analogs of the author's results are obtained for the classes $L_{\beta}^{\psi} \mathfrak{R}$.
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| first_indexed | 2026-03-24T03:23:16Z |
| format | Article |
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| id | umjimathkievua-article-5870 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:23:16Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/8d/b358cd5497964e280653b392cac6818d.pdf |
| spelling | umjimathkievua-article-58702020-03-19T09:19:41Z Approximation of cauchy-type integrals in Jordan domains Приближение интегралов типа Коши в жордановых областях Stepanets, O. I. Степанец, А. И. Степанец, А. И. The concept of a generalized ψ-derivative of a function of a complex variable is introduced and applied to classify functions analytic in Jordan domains. The approximations of functions from the classes introduced by this procedure are studied by using algebraic polynomials constructed on the basis of the Faber polynomials after the summation of Faber series. Analogs of the author's results are obtained for the classes $L_{\beta}^{\psi} \mathfrak{R}$. Вводиться поняття узагальненої ψ-похідної функції комплексної змінної, на базі чого проводиться класифікація функцій, аналітичних в жорданових областях. Вивчаються наближення функцій з таким чином введених класів за допомогою многочленів, побудованих на основі многочленів Фабера шляхом підсумовування рядів Фабера. Одержані аналоги результатів автора для класів $L_{\beta}^{\psi} \mathfrak{R}$ в періодичному випадку. Institute of Mathematics, NAS of Ukraine 1993-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5870 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 6 (1993); 809–833 Український математичний журнал; Том 45 № 6 (1993); 809–833 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5870/8423 https://umj.imath.kiev.ua/index.php/umj/article/view/5870/8424 Copyright (c) 1993 Stepanets O. I. |
| spellingShingle | Stepanets, O. I. Степанец, А. И. Степанец, А. И. Approximation of cauchy-type integrals in Jordan domains |
| title | Approximation of cauchy-type integrals in Jordan domains |
| title_alt | Приближение интегралов типа Коши в жордановых областях |
| title_full | Approximation of cauchy-type integrals in Jordan domains |
| title_fullStr | Approximation of cauchy-type integrals in Jordan domains |
| title_full_unstemmed | Approximation of cauchy-type integrals in Jordan domains |
| title_short | Approximation of cauchy-type integrals in Jordan domains |
| title_sort | approximation of cauchy-type integrals in jordan domains |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5870 |
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