Best approximation by holomorphic functions. Application to the best polynomial approximation of classes of holomorphic functions
We find necessary and sufficient conditions under which a real function from $L_p(\mathbb{T}),\; 1 \leq p < \infty$, is badly approximable by the Hardy subspace $H_p^0: = \{f \in H_p:\; F(0) = 0\}$. In a number of cases, we obtain exact values for the best approximations in the mean of funct...
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| Date: | 2007 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2007
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3369 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We find necessary and sufficient conditions under which a real function from $L_p(\mathbb{T}),\; 1 \leq p < \infty$, is badly approximable by the Hardy subspace $H_p^0: = \{f \in H_p:\; F(0) = 0\}$. In a number of cases, we obtain exact values for the best
approximations in the mean of functions holomorphic in the unit disk by functions that are holomorphic outside the unit disk.
We use obtained results in determining exact values of the best polynomial approximations and га-widths of some classes of holomorphic functions.
We find necessary and sufficient conditions under which the generalized Bernstein inequality for algebraic polynomials on the unit circle is true.
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