Estimates for certain approximation characteristics of Nikol'skii-Besov spaces with generalized mixed smoothness
type: Item
instance of: scholarly article
title: Estimates for certain approximation characteristics of Nikol'skii-Besov spaces with generalized mixed smoothness
zbMATH Open document ID: 1184.41016
DOI: 10.1134/S1064562409030028
author: D. B. Bazarkhanov
published in: Doklady Mathematics
publication date: 2009-10-26T00:00:00Z
review text: The author presents (without proofs) sharp estimates for approximations by Fourier sums, for the best \(N\)-term trigonometric approximations, and for the trigonometric and Kolmogorov widths of the unit ball in the Nikolskii-Besov space \(MB^{s,\varepsilon}_{p\theta} (\mathbb T^d)\) of generalized mixed smoothness (\(s\in (0,\infty)^n\), \(1<p<\infty\), \(1\leq\theta\leq\infty\), \(1\leq n \leq d\)) in the metric of the space \(L_q (\mathbb T^d)\) \((1<q<\infty)\). Aperiodic analogues of the first three characteristics are also considered.
reviewed by: Bohumír Opic
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 42B99
zbMATH DE Number: 5621444
zbMATH Keywords: Nikol'skii-Besov spaces with generalized mixed smoothness
zbMATH Keywords: approximations by Fourier sums
zbMATH Keywords: trigonometric approximations
zbMATH Keywords: trigonometric and Kolmogorov widths
MaRDI profile type: Publication
cites work: Q4348451
cites work: Nonlinear methods of approximation
cites work: Approximation of the Besov classes of periodic functions of several variables in the space \(L_ q\)
cites work: Average widths of Sobolev classes on \(\mathbb{R}^ n\)
cites work: Spaces of functions of mixed smoothness and approximation from hyperbolic crosses
cites work: Average widths fo Sobolev-Wiener classes with mixed smoothness in \(L_q(\mathbb{R}^d)\)
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description: scientific article; zbMATH DE number 5621444