Best approximation and best unilateral approximation of the kernel of a biharmonic equation and optimal renewal of the values of operators
For the classB p ρ , 0 ≤ ρ < 1, 1≤p ≤ ∞, of 2π-periodic functions of the form f(t)=u(ρ,t), whereu (ρ,t) is a biharmonic function in the unit disk, we obtain the exact values of the best approximation and best unilateral approximation of the kernel Kρ(t) of the convolution f= Kρ *g, ∥g∥ρ≤l,...
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| Дата: | 1995 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1995
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5546 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511779130441728 |
|---|---|
| author | Shabozov, M. Sh. Шабозов, М. Ш. Шабозов, М. Ш. |
| author_facet | Shabozov, M. Sh. Шабозов, М. Ш. Шабозов, М. Ш. |
| author_sort | Shabozov, M. Sh. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:13:12Z |
| description | For the classB p ρ , 0 ≤ ρ < 1, 1≤p ≤ ∞, of 2π-periodic functions of the form f(t)=u(ρ,t), whereu (ρ,t) is a biharmonic function in the unit disk, we obtain the exact values of the best approximation and best unilateral approximation of the kernel Kρ(t) of the convolution f= Kρ *g, ∥g∥ρ≤l, with respect to the metric of L1. We also consider the problem of renewal of the values of the convolution operator by using the information about the values of the boundary functions. |
| first_indexed | 2026-03-24T03:18:19Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5546 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:18:19Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/d9/4074f4ae292d51c1422aee30ed134ed9.pdf |
| spelling | umjimathkievua-article-55462020-03-19T09:13:12Z Best approximation and best unilateral approximation of the kernel of a biharmonic equation and optimal renewal of the values of operators Наилучшее и наилучшее односторонее приближения ядра бигармонического уравнения и оптимальное восстановление значений операторов Shabozov, M. Sh. Шабозов, М. Ш. Шабозов, М. Ш. For the classB p ρ , 0 ≤ ρ < 1, 1≤p ≤ ∞, of 2π-periodic functions of the form f(t)=u(ρ,t), whereu (ρ,t) is a biharmonic function in the unit disk, we obtain the exact values of the best approximation and best unilateral approximation of the kernel Kρ(t) of the convolution f= Kρ *g, ∥g∥ρ≤l, with respect to the metric of L1. We also consider the problem of renewal of the values of the convolution operator by using the information about the values of the boundary functions. Для класу $B_p^{ρ},\; 0 ≤ ρ < 1, 1 ≤ p ≤ ∞,$ $2π$-періодичних функцій вигляду $f(t) = u(ρ,t)$, де $(ρ,t)$— бігармонічна функція в одиничному колі, знайдено точні значення найкращого та найкращого односторонього наближень ядра $K_{ρ}(t)$ згортки $f= K_{ρ}*g,\; ∥g∥_{ρ} ≤ l$ у метриці $L_1$. Розглянута задача відновлення значень оператора згортки згідно з інформацією про значення граничних функцій. Institute of Mathematics, NAS of Ukraine 1995-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5546 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 11 (1995); 1549–1557 Український математичний журнал; Том 47 № 11 (1995); 1549–1557 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5546/7780 https://umj.imath.kiev.ua/index.php/umj/article/view/5546/7781 Copyright (c) 1995 Shabozov M. Sh. |
| spellingShingle | Shabozov, M. Sh. Шабозов, М. Ш. Шабозов, М. Ш. Best approximation and best unilateral approximation of the kernel of a biharmonic equation and optimal renewal of the values of operators |
| title | Best approximation and best unilateral approximation of the kernel of a biharmonic equation and optimal renewal of the values of operators |
| title_alt | Наилучшее и наилучшее односторонее приближения ядра бигармонического уравнения и оптимальное восстановление значений операторов |
| title_full | Best approximation and best unilateral approximation of the kernel of a biharmonic equation and optimal renewal of the values of operators |
| title_fullStr | Best approximation and best unilateral approximation of the kernel of a biharmonic equation and optimal renewal of the values of operators |
| title_full_unstemmed | Best approximation and best unilateral approximation of the kernel of a biharmonic equation and optimal renewal of the values of operators |
| title_short | Best approximation and best unilateral approximation of the kernel of a biharmonic equation and optimal renewal of the values of operators |
| title_sort | best approximation and best unilateral approximation of the kernel of a biharmonic equation and optimal renewal of the values of operators |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5546 |
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