Weighted approximation with varying weights: The case of a power-type singularity
type: Item
instance of: scholarly article
title: Weighted approximation with varying weights: The case of a power-type singularity
zbMATH Open document ID: 0962.41002
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-02-27T00:00:00Z
review text: This paper is a continuation of recent work by the author himself [Constructive Approximation 12, No. 2, 287-301 (1996; Zbl 0864.41006) and ibid. 87, No. 1, 112-115 (1996; Zbl 0862.41006)] and by \textit{L. Totik} [Weighted Approximation with varying weight (1994; Zbl 0808.41001)]. The following type of generalized Weierstraß problem is considered: Characterize the class of functions \(f\) that can be uniformly approximated by weighted polynomials of the form \(w^n p_n\), \(p_n\in\Pi_n\). Denoting by \(\mu_w\) the extremal measure associated with \(w\) the central result of the paper can be stated as follows: If in a neighborhood of a point \(t_0\mu_w\) has a density with a power-type singularity at \(t_0\), then every function \(f\) of the above type vanishes at \(t_0\).
reviewed by: Guido Walz
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A30
zbMATH DE Number: 1005643
zbMATH Keywords: weighted approximation
zbMATH Keywords: power-type singularity
author: Arno B. J. Kuijlaars
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0444
OpenAlex ID: W1984661673
DOI: 10.1006/JMAA.1996.0444
Recommended article: Q5716198
Recommended article: Q3433597
Recommended article: Weighted Approximation of Functions with Inner Singularities by Exponential Weights in [−1, 1]
Recommended article: Weighted approximation of functions with singularities by combinations of Bernstein operators
Recommended article: Weighted approximation of functions with singularities by Bernstein operators
Recommended article: Weighted approximation by Bernstein quasiinterpolants for functions with singularities
Recommended article: Q2992058
Recommended article: On weighted approximation by rational operators for functions with singularities
Recommended article: A note on weighted polynomial approximation with varying weights
Recommended article: On Weighted Approximation by Modified Bernstein Operators for Functions with Singularities
description: scientific article; zbMATH DE number 1005643