Best approximation by holomorphic functions. Application to the best polynomial approximation of classes of holomorphic functions

• Date: 2007
• Main Authors: Savchuk, V. V., Савчук, В. В.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2007
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3369
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...