The degree of approximation by polynomials on some disjoint intervals in the complex plane
type: Item
instance of: scholarly article
title: The degree of approximation by polynomials on some disjoint intervals in the complex plane
zbMATH Open document ID: 1107.30030
author: Maurice Hasson
published in: Journal of Approximation Theory
publication date: 2007-02-14T00:00:00Z
review text: Let \(f\) be a continuous function defined on the compact set \(K\) consisting of the union of several disjoint intervals in the complex plane. Using the overconvergence technique the author estimates lower bounds of the error \(E_n(f,K)=\inf_{P\in {\mathcal{P}}_n}\| f-P\|\) where inf is taken over all polynomials of degree at most \(n\). He obtains also the convergence result for this class of functions proving the formulae for \(\limsup_{n\rightarrow\infty} (E_n(f,K))^{\frac{1}{n}}\). In addition, his proof provides an algorithm to build the polynomial of near best approximation. This work was motivated by problems occuring in digital signal processing where approximation by polynomials on disjoint intervals is used for the dessign of digital filters.
reviewed by: Jacek Gilewicz
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A29
Mathematics Subject Classification ID: 41A40
zbMATH DE Number: 5125997
zbMATH Keywords: Complex approximation
zbMATH Keywords: Degree of approximation
zbMATH Keywords: Conformal mapping
MaRDI profile type: Publication
full work available at URL: j.jat.2006.05.003
OpenAlex ID: W2038128354
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DOI: 10.1016/J.JAT.2006.05.003
description: scientific article; zbMATH DE number 5125997