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Mean dimension, widths, and optimal recovery of Sobolev classes of functions on the line
Sbornik. Mathematics, Tome 74 (1993) no. 2, pp. 381-403 Cet article a éte moissonné depuis la source Math-Net.Ru

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The concept of mean dimension is introduced for a broad class of subspaces of $L_p(\mathbf R)$, and analogues of the Kolmogorov widths, Bernstein widths, Gel'fand widths, and linear widths are defined. The precise values of these quantities are computed for Sobolev classes of functions on $\mathbf R$ in compatible metrics, and the corresponding extremal spaces and operators are described. A closely related problem of optimal recovery of functions in Sobolev classes is also studied. 
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G. G. Magaril-Il'yaev. Mean dimension, widths, and optimal recovery of Sobolev classes of functions on the line. Sbornik. Mathematics, Tome 74 (1993) no. 2, pp. 381-403. http://geodesic.mathdoc.fr/item/SM_1993_74_2_a5/

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