Necessary and sufficient conditions for mean convergence of orthogonal expansions for Freud weights
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions for mean convergence of orthogonal expansions for Freud weights
zbMATH Open document ID: 0847.42023
DOI: 10.1007/BF01208559
author: S. W. Jha
author: Doron S. Lubinsky
published in: Constructive Approximation
publication date: 1996-10-15T00:00:00Z
review text: In a classic paper, B. Muckenhoupt established necessary and sufficient conditions for weighted \(L_p\) convergence of Hermite series, i.e., orthogonal expansions in Hermite polynomials. In the paper under review, the Hermite polynomials are replaced by systems of orthogonal polynomials that can be considered as natural generalizations. The new polynomials are orthogonal with respect to a class of Freud weights \(W^2:= e^{- 2Q}\). For the convergence of expansions in these polynomials necessary and sufficient conditions are obtained that are identical with those proved by Muckenhoupt. The necessary condition applies when \(Q(x)= |x|^\alpha\), \(\alpha> 1\), while the sufficient one applies for \(\alpha= 2, 4, 6,\dots\;\).
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 810114
zbMATH Keywords: orthogonal expansions
zbMATH Keywords: Freud weights
reviewed by: Herbert Stahl
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01208559
OpenAlex ID: W2052943928
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description: scientific article; zbMATH DE number 810114