The best polynomial approximations of some classes of analytic functions in the Hardy spaces

S.B. Vakarchuk; V.I. Zabutna; M.B. Vakarchuk

doi:10.15421/241802

The best polynomial approximations of some classes of analytic functions in the Hardy spaces

S.B. Vakarchuk (Alfred Nobel University), https://orcid.org/0000-0002-2562-8844
V.I. Zabutna (Oles Honchar Dnipro National University)
M.B. Vakarchuk (Oles Honchar Dnipro National University)

Abstract

Problems of the best polynomial approximation of classes of analytic functions $$$H^m_{p,R}$$$, $$$m\in \mathbb{Z}_+$$$, $$$R \geqslant 1$$$, $$$1 \leqslant p \leqslant \infty$$$, have been investigated in the Hardy spaces $$$H_p$$$. The best linear methods of approximation were constructed on the indicated classes.

Keywords

analytic function; best polynomial approximation; modulus of continuity; best linear method of approximation; Hardy space

MSC 2020

41A10; 30H10; 30E10; 41A50

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