Forward and converse theorems of polynomial approximation for exponential weights on \([-1,1]\). I
type: Item
instance of: scholarly article
title: Forward and converse theorems of polynomial approximation for exponential weights on \([-1,1]\). I
zbMATH Open document ID: 0887.41014
published in: Journal of Approximation Theory
publication date: 1998-03-30T00:00:00Z
review text: The author proves Jackson theorems in weighted \(L_p\)-spaces on \([-1,1]\), \(0<p\leq \infty\), where the weights have not a behaviour like Jacobi weights, but are exponential functions of the form \(\exp(-Q(x))\), \(Q\) an even function that grows faster than \((1-x^2)^{-\alpha}\) near \(\pm 1\) for some \(\alpha >0\). These Jackson theorems are given in terms of moduli of continuity defined in the paper and require many previous technical results. The author announces a second part for the relationship of moduli of the continuity with the theory of \(K\)-functionals as well as for the study of the converse theorems.
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 1076152
zbMATH Keywords: Jackson and Bernstein theorems
zbMATH Keywords: weighted \(L_ p\)-spaces
zbMATH Keywords: moduli of continuity
author: Doron S. Lubinsky
reviewed by: Miguel A. Jiménez
MaRDI profile type: Publication
full work available at URL: jath.1996.3087
OpenAlex ID: W4213122937
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DOI: 10.1006/JATH.1996.3087
description: scientific article; zbMATH DE number 1076152