Wavelet approximation and Fourier widths of classes of periodic functions of several variables. I
type: Item
instance of: scholarly article
title: Wavelet approximation and Fourier widths of classes of periodic functions of several variables. I
zbMATH Open document ID: 1219.42025
DOI: 10.1134/S0081543810020021
author: D. B. Bazarkhanov
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2010-11-15T00:00:00Z
review text: Characterizations and special norm equivalences of function spaces \(B_{pq}^{sm} (I^{k}) \) and \(L_{pq}^{sm}(I^{k})\) of Nikol'skii-Besov and Lizorkin-Triebel types are studied, where \(I\) denotes the real numbers \({\mathbb R}\) or the torus. More exactly, wavelet expansions using Meyer wavelets are considered, and the equivalence of norms in these function spaces with discrete norms of sequences of wavelet coefficients is shown. The author establishes order-sharp estimates for the approximation of functions in \(B_{pq}^{sm} (I^{k}) \) and \(L_{pq}^{sm}(I^{k})\) by special partial sums of these series in the metric \(L_{r}(I^{k})\) for a number of relations between the parameters \(s,p,q,r\), and \(m\), where \(s=(s_{1}, \dots , s_{n}) \in {\mathbb R}_{+}^{n}\), \(1 \leq p,q,r \leq \infty\), \(m= (m_{1}, \dots , m_{n}) \in {\mathbb N}^{n}\), and \(k=m_{1}+ \dots + m_{n}\). In the periodic case, the Fourier widths of these function classes are studied.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 5816191
zbMATH Keywords: Nikol'skii-Besov spaces
zbMATH Keywords: Lizorkin-Triebel spaces
zbMATH Keywords: Meyer wavelets
reviewed by: Gerlind Plonka
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5816191