Widths between the anisotropic spaces and the spaces of functions with mixed smoothness
type: Item
instance of: scholarly article
title: Widths between the anisotropic spaces and the spaces of functions with mixed smoothness
zbMATH Open document ID: 1237.41011
published in: Journal of Approximation Theory
publication date: 2012-02-25T00:00:00Z
review text: The main focus of the paper is on the derivation of sharp asymptotic orders of the Kolmogorov, Gelfand, linear, and orthoprojection widths of the classes \(BF^r_{\text{mix}, p}\) in the anisotropic space \(F^{\mathbf{R}}_q\) and those of the classes \(BF^{\mathbf {R}}_q\) in the space \(F^r_{\text{mix},q}\), for all \(p,q\in [1, \infty]\). Here, \(F^r_{\text{mix},q}\) denotes either the Sobolev space \(W^r_{\text{mix},q}\) of mixed smoothness or the Hölder-Nikolskii space \(H^r_{\text{mix},q}\) of mixed smoothness, and \(F^{\mathbf {R}}_q\) either the anisotropic Sobolev space \(W^{\mathbf{R}}_q\) or the anisotropic Hölder-Nikolskij space \(H^{\mathbf{R}}_q\). The quantities \(BF^{\mathbf {R}}_q\) and \(BF^{\mathbf {R}}_q\) represent the unit ball of the spaces \(F^r_{\text{mix},q}\) and \(F^{\mathbf {R}}_q\), respectively.
Mathematics Subject Classification ID: 41A46
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 6009280
zbMATH Keywords: Kolmogorov widths
zbMATH Keywords: Gelfand widths
zbMATH Keywords: linear widths
zbMATH Keywords: orthoprojection widths
zbMATH Keywords: anisotropic spaces
zbMATH Keywords: spaces of functions with mixed smoothness
author: Heping Wang
reviewed by: Peter Massopust
MaRDI profile type: Publication
full work available at URL: j.jat.2011.11.006
OpenAlex ID: W2069563135
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DOI: 10.1016/J.JAT.2011.11.006
description: scientific article; zbMATH DE number 6009280