Estimates of the Kolmogorov Widths of Classes of Analytic Functions Representable by Cauchy-Type Integrals. II
In normed spaces of functions analytic in the Jordan domain Ω⊂ℂ, we establish exact order estimates for the Kolmogorov widths of classes of functions that can be represented in Ω by Cauchy-type integrals along Γ = ∂Ω with densities f(·) such that \(f \circ \Psi \in L_{\beta ,p}^\Psi (T)\) . Here,...
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| Date: | 2001 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2001
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4257 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510389052112896 |
|---|---|
| author | Romanyuk, V. S. Романюк, В. С. |
| author_facet | Romanyuk, V. S. Романюк, В. С. |
| author_sort | Romanyuk, V. S. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:25:15Z |
| description | In normed spaces of functions analytic in the Jordan domain Ω⊂ℂ, we establish exact order estimates for the Kolmogorov widths of classes of functions that can be represented in Ω by Cauchy-type integrals along Γ = ∂Ω with densities f(·) such that \(f \circ \Psi \in L_{\beta ,p}^\Psi (T)\) . Here, Ψ is a conformal mapping of \(C\backslash \overline \Omega \) onto {w: |w| > 1}, and \(L_{\beta ,p}^\Psi (T)\) is a certain subset of infinitely differentiable functions on T = {w: |w| = 1}. |
| first_indexed | 2026-03-24T02:56:13Z |
| format | Article |
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| id | umjimathkievua-article-4257 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:56:13Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/e1/45a5311a08b3b3f3583cf71dd2d391e1.pdf |
| spelling | umjimathkievua-article-42572020-03-18T20:25:15Z Estimates of the Kolmogorov Widths of Classes of Analytic Functions Representable by Cauchy-Type Integrals. II Оценки колмогоровских поперечников классов аналитических функций, представимых интегралами типа Коши. II Romanyuk, V. S. Романюк, В. С. In normed spaces of functions analytic in the Jordan domain Ω⊂ℂ, we establish exact order estimates for the Kolmogorov widths of classes of functions that can be represented in Ω by Cauchy-type integrals along Γ = ∂Ω with densities f(·) such that \(f \circ \Psi \in L_{\beta ,p}^\Psi (T)\) . Here, Ψ is a conformal mapping of \(C\backslash \overline \Omega \) onto {w: |w| > 1}, and \(L_{\beta ,p}^\Psi (T)\) is a certain subset of infinitely differentiable functions on T = {w: |w| = 1}. У нормованих просторах функцій, аналітичних в жордановій області Ω⊂ℂ , встановлено точні за порядком оцінки поперечників за Колмогоровим класів функцій, що зображуються в Ω інтегралами типу Коші вздовж Γ = ∂Ω зі щільностями f(·), для яких \(f \circ \Psi \in L_{\beta ,p}^\Psi (T)\) , де Ψ — конформне відображення \(C\backslash \overline \Omega \) на {w: |w| > 1}, a \(L_{\beta ,p}^\Psi (T)\) — деяка підмножина нескінченно диференційовних функцій на T = {w: |w| = 1}. Institute of Mathematics, NAS of Ukraine 2001-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4257 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 3 (2001); 346-355 Український математичний журнал; Том 53 № 3 (2001); 346-355 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4257/5218 https://umj.imath.kiev.ua/index.php/umj/article/view/4257/5219 Copyright (c) 2001 Romanyuk V. S. |
| spellingShingle | Romanyuk, V. S. Романюк, В. С. Estimates of the Kolmogorov Widths of Classes of Analytic Functions Representable by Cauchy-Type Integrals. II |
| title | Estimates of the Kolmogorov Widths of Classes of Analytic Functions Representable by Cauchy-Type Integrals. II |
| title_alt | Оценки колмогоровских поперечников классов аналитических функций, представимых интегралами типа Коши. II |
| title_full | Estimates of the Kolmogorov Widths of Classes of Analytic Functions Representable by Cauchy-Type Integrals. II |
| title_fullStr | Estimates of the Kolmogorov Widths of Classes of Analytic Functions Representable by Cauchy-Type Integrals. II |
| title_full_unstemmed | Estimates of the Kolmogorov Widths of Classes of Analytic Functions Representable by Cauchy-Type Integrals. II |
| title_short | Estimates of the Kolmogorov Widths of Classes of Analytic Functions Representable by Cauchy-Type Integrals. II |
| title_sort | estimates of the kolmogorov widths of classes of analytic functions representable by cauchy-type integrals. ii |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4257 |
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