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,...
Збережено в:
| 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 |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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. |
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