Kolmogorov widths of weighted Sobolev classes on a domain for a special class of weights
type: Item
instance of: scholarly article
title: Kolmogorov widths of weighted Sobolev classes on a domain for a special class of weights
zbMATH Open document ID: 1272.46029
DOI: 10.1134/S1061920811030083
author: A. A. Vasil'eva
published in: Russian Journal of Mathematical Physics
publication date: 2012-10-22T00:00:00Z
review text: Let \(X,Y\) be a normed spaces, \(M\subset X\). For \(n \in \mathbb{Z}\), let \(\mathcal {L}_n(X)\) be the family of all subspaces of \(X\) of dimension \(n\). The Kolmogorov \(n\)-width and the linear \(n\)-width are defined by \[ d_n(M,X)=\inf_{L\in \mathcal{L}_n(X)}\sup_{x\in M}\inf_{y\in L}\|x-y\|, \quad \lambda _n(M,X)=\inf_{A\in L(X,Y),\text{rk}A\leq n}\sup_{x\in M}\|x-Ax\|, \] respectively. For \(A\in L(X,Y)\), the approximation numbers are defined by \[ {\mathcal A} _n(A)=\inf_{A_n\in L(X,Y),\text{ rk} A_n\leq n}\sup_{x\in M}\|A-A_n\|. \] If \(X\) and \(Y\) represent certain weighted Sobolev classes and corresponding weighted Lebesgue spaces over a bounded domain \(\Omega \) in \(\mathbb{R}^d\), respectively, such that the embedding is compact, relations between Kolmogorov \(n\)-width, linear \(n\)-width and approximation numbers are obtained.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 41A46
Mathematics Subject Classification ID: 47B06
zbMATH DE Number: 6097095
zbMATH Keywords: weighted Sobolev classes
zbMATH Keywords: Kolmogorov \(n\)-width
zbMATH Keywords: linear \(n\)-width
zbMATH Keywords: approximation numbers
MaRDI profile type: Publication
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full work available at URL: s1061920811030083
OpenAlex ID: W1966270485
description: scientific article; zbMATH DE number 6097095