Linear methods for approximation of some classes of holomorphic functions from the Bergman space
We construct a linear method of the approximation $ \{Q_{n,\psi} \}_{n \in {\mathbb N}}$ in the unit disk of classes of holomorphic functions $A^{\psi}_p$ that are the Hadamard convolutions of unit balls of the Bergman space $A_p$ with reproducing kernels $\psi(z) = \sum^\infty_{k=0}\psi_k z^k....
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| Дата: | 2008 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2008
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3196 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We construct a linear method of the approximation $ \{Q_{n,\psi} \}_{n \in {\mathbb N}}$
in the unit disk of classes of holomorphic functions $A^{\psi}_p$ that are the Hadamard
convolutions of unit balls of the Bergman space $A_p$
with reproducing kernels $\psi(z) = \sum^\infty_{k=0}\psi_k z^k.$
We give conditions on $\psi$ under which the method
$ \{Q_{n,\psi} \}_{n \in {\mathbb N}}$ approximate the class $A^{\psi}_p$ in metrics of
the Hardy space $H_s$ and Bergman space $A_s,\; 1 \leq s \leq p,$
with error that coincides in order with a value of the best approximation by algebraic polynomials. |
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