Best approximation of functions on the ball on the weighted Sobolev space equipped with a Gaussian measure
type: Item
instance of: scholarly article
title: Best approximation of functions on the ball on the weighted Sobolev space equipped with a Gaussian measure
zbMATH Open document ID: 1205.41031
author: Xuebo Zhai
author: Heping Wang
published in: Journal of Approximation Theory
publication date: 2010-06-25T00:00:00Z
review text: This paper contains two parts. In the first part, the authors obtain relations between the classical and \(p\)-average Kolmogorov widths for all \(p\), \(0 < p < \infty\), which is a generalization of the corresponding results of \textit{J. Creuzig} [J. Complexity 18, No. 1, 287--303 (2002; Zbl 1008.41020)]. The second part of the paper is devoted to the study of the best approximation by polynomial subspaces on Weighted Sobolev space of functions on the unit ball \({\mathcal B}^d\) with a Gaussian measure. The authors obtain average error estimates of the best approximation by polynomial subspaces in the weighted \(L_q\) space for \(1 \leq q < \infty\), and find that in the average case setting, whether or not the polynomial subspaces are the asymptotically optimal subspaces in the weighted \(L_q\) space for \(1 \leq q < \infty\) depends on the weight and is independent of the dimension \(d\).
reviewed by: Richard A. Zalik
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 41A46
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 5726581
zbMATH Keywords: best approximation
zbMATH Keywords: average width
zbMATH Keywords: weighted Sobolev space
zbMATH Keywords: Gaussian measure
MaRDI profile type: Publication
full work available at URL: j.jat.2009.12.004
OpenAlex ID: W2008977056
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DOI: 10.1016/J.JAT.2009.12.004
description: scientific article; zbMATH DE number 5726581