Bounds and inequalities for arbitrary orthogonal polynomials on finite intervals
type: Item
instance of: scholarly article
title: Bounds and inequalities for arbitrary orthogonal polynomials on finite intervals
zbMATH Open document ID: 0823.42012
author: Yingguang Shi
published in: Journal of Approximation Theory
publication date: 1995-10-25T00:00:00Z
review text: It seems that the main goal of this paper is to improve results of the author's previous paper [J. Approximation Theory 73, No. 3, 303-335 (1993; Zbl 0780.42017)] concerning bounds and inequalities for the orthogonal polynomials with respect to the measure \(d\alpha\), where \(\alpha\) is a nondecreasing function on \([-1,1]\) with infinitely many points of increase such that all moments of \(d\alpha\) are finite. The key tool for this improvement is the observation that for any measure \(d\alpha\) supported in \([-1,1]\) there exists a positive \(\delta< 2\) such that \[ \textstyle{\inf_{\Omega\text{ (Lebesgue measurable) }\subset [- 1, 1],|\Omega|= \delta}}\Biggl\{\int_ \Omega d\alpha(x)\Biggl/\int_{[- 1,1]} d\alpha(x)\Biggr\}> 0. \] {}.
reviewed by: Wiesław Pleśniak
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 756616
zbMATH Keywords: finite intervals
zbMATH Keywords: Lagrange and Hermite-Fejér interpolation polynomials
zbMATH Keywords: bounds
zbMATH Keywords: inequalities
zbMATH Keywords: orthogonal polynomials
MaRDI profile type: Publication
full work available at URL: jath.1995.1046
OpenAlex ID: W4210589303
DOI: 10.1006/JATH.1995.1046
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description: scientific article; zbMATH DE number 756616