Polynomial approximation of piecewise analytic functions
type: Item
instance of: scholarly article
title: Polynomial approximation of piecewise analytic functions
zbMATH Open document ID: 0876.41015
author: Dieter Gaier
published in: The Journal of Analysis
publication date: 1997-12-02T00:00:00Z
review text: Let the function \(f\) be continuous on \([-1,1]\) and ``piecewise analytic'' there in some sense. Then \textit{K. G. Ivanov}, \textit{E. B. Saff} and \textit{V. Totik} [Proc. Am. Math. Soc. 106, No. 1, 153-161 (1989; Zbl 0668.41006)] and \textit{E. B. Saff} and \textit{V. Totik} [J. Lond. Math. Soc., II. Ser. 39, 487-498 (1989; Zbl 0683.41011)] proved the existence of polynomials \(p_n\) of degree \(n\) which are ``almost best approximating'' \(f\) uniformly on \([-1,1]\) and in addition admit a geometric convergence rate in points, where \(f\) itself is analytic. Here, the author gives another more constructive approach to results of this kind by projecting the problems onto the unit circle and by use of summability methods, and he improves some of the above results.
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 1002154
zbMATH Keywords: approximation by polynomials
zbMATH Keywords: degree of approximation
reviewed by: Klaus Menke
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1002154