Geodesic
The widths of classes of analytic functions in a disc
Sbornik. Mathematics, Tome 201 (2010) no. 8, pp. 1091-1110 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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