Approximation by weighted polynomials
type: Item
instance of: scholarly article
title: Approximation by weighted polynomials
zbMATH Open document ID: 1029.41002
DOI: 10.1016/S0021-9045(02)00017-5
author: D. Benko
published in: Journal of Approximation Theory
publication date: 2003-04-02T00:00:00Z
review text: The paper is devoted to the study of approximation by weighted polynomials. The author proves that if \(xQ'(x)\) is increasing on \((0,\infty)\) and \(w(x)= \exp(-Q(x))\) is the corresponding weight on \([0,\infty)\), then every continuous function that vanishes outside. The support of the extremal measure associated with \(w\) can be uniformly approximated by weighted polynomials of the form \(w^nP_n\). In connection with the Borwein-Saff conjecture Totik [\textit{V. Totik} Constructive Approximation 16, 261-281 (2000; Zbl 0955.41005)] proved a similar result for convex \(Q\).
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 1891281
zbMATH Keywords: approximation by weighted polynomials
zbMATH Keywords: convex function
zbMATH Keywords: uniform approximation
zbMATH Keywords: continuous function
reviewed by: S. M. Mazhar
MaRDI profile type: Publication
cites work: A note on weighted polynomial approximation with varying weights
cites work: The role of the endpoint in weighted polynomial approximation with varying weights
cites work: Strong asymptotics for extremal polynomials associated with weights on \({\mathbb{R}}\)
cites work: Q4360405
cites work: Weighted approximation with varying weight
cites work: Weighted polynomial approximation for convex external fields
description: scientific article; zbMATH DE number 1891281