The relative \(n\)-widths of Sobolev classes with restrictions
type: Item
instance of: scholarly article
title: The relative \(n\)-widths of Sobolev classes with restrictions
zbMATH Open document ID: 1165.41006
published in: Journal of Approximation Theory
publication date: 2009-04-08T00:00:00Z
review text: For the Sobolev classes \(W^1_p[0,1]\), this paper deals with the relative \(n\)-width of the set \(B_p^1=\{f \in W^1_p: f(0)=0\}\). It is shown that, for various values of \(p,q\), \(d_n(B^1_p,B^1_p)_q\) is equal to \(\frac{\sup\{\|f\|_q [0,1]: f \in B^1_p\}}{2n}\).
Mathematics Subject Classification ID: 41A46
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 5541720
zbMATH Keywords: Sobolev classes
zbMATH Keywords: relative \(n\)-width
author: Guiqiao Xu
reviewed by: T.S.S.R.K. Rao
MaRDI profile type: Publication
full work available at URL: j.jat.2008.05.003
OpenAlex ID: W1973975053
cites work: Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse
cites work: Q3344608
cites work: Q4320142
cites work: Q5511094
cites work: Q4273944
cites work: The best \(L_ 1\)-approximations by splines in the presence of restrictions on their derivatives
cites work: On best uniform approximation by splines in the presence of restrictions on their derivatives
cites work: Q5687804
cites work: Q3801999
cites work: Q5535819
cites work: Q5602378
cites work: Approximation of Sobolev classes by their finite-dimensional sections
cites work: Q4782476
cites work: Q5186127
cites work: Q5569260
cites work: ON A METHOD FOR ESTIMATION FROM BELOW OF DIAMETERS OF SETS IN BANACH SPACES
cites work: Exact values of relative widths of classes of differentiable functions
cites work: Q5754098
DOI: 10.1016/J.JAT.2008.05.003
description: scientific article; zbMATH DE number 5541720