The widths of classes of analytic functions in a~disc
Sbornik. Mathematics, Tome 201 (2010) no. 8, pp. 1091-1110
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The precise values of several $n$-widths of the classes $W^m_{p,R}(\Psi)$, $1\leqslant p\infty$, $m\in\mathbb N$, $R\geqslant1$, in the Banach spaces $\mathscr L_{p,\gamma}$ and $B_{p,\gamma}$ are calculated, where $\gamma$ is a weight. These are classes of analytic functions $f$ in a disc of radius $R$ whose $m$th derivatives $f^{(m)}$ belong to the Hardy space $H_{p,R}$ and whose angular boundary values have averaged moduli of smoothness of second order which are majorized by the fixed function $\Psi$ on the point set
$\{\pi/(2k)\}_{k\in\mathbb N}$. For the classes $W^m_{p,R}(\Psi)$ best linear methods of approximation in $\mathscr L_{p,\gamma}$ are developed. Extremal problems of related content are also considered. Bibliography: 37 titles.
Keywords:
weight function, best linear method of approximation, optimal method of function recovery, best method of coding of functions.
@article{SM_2010_201_8_a0,
author = {S. B. Vakarchuk and M. Sh. Shabozov},
title = {The widths of classes of analytic functions in a~disc},
journal = {Sbornik. Mathematics},
pages = {1091--1110},
publisher = {mathdoc},
volume = {201},
number = {8},
year = {2010},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2010_201_8_a0/}
}
S. B. Vakarchuk; M. Sh. Shabozov. The widths of classes of analytic functions in a~disc. Sbornik. Mathematics, Tome 201 (2010) no. 8, pp. 1091-1110. http://geodesic.mathdoc.fr/item/SM_2010_201_8_a0/