A local version of the Pawłucki-Pleśniak extension operator
type: Item
instance of: scholarly article
title: A local version of the Pawłucki-Pleśniak extension operator
zbMATH Open document ID: 1075.46022
published in: Journal of Approximation Theory
publication date: 2005-02-22T00:00:00Z
review text: Let \(K\) be a perfect compact set on the line \(\mathbb{R}\) and let \(E(K)\) denote the space of all functions \(f\) on \(K\) that are extendable to some \(F\in C^\infty(\mathbb{R})\). Various methods have been devised for constructing continuous extension operator \(L\) such that \(L(f)= F\). One such method described by \textit{W. Plešniak} [J. Approximation Theory 61, 106--117 (1990; Zbl 0702.41023)] used Lagrange interpolation and required that \(K\) satisfy Markov's inequality. In the present paper, the authors construct \(L\) using local Lagrange interpolation on certain generalized Cantor-type sets \(K\) which do not require Markov's inequality. They rely upon earlier work of \textit{A. Goncharov} [Stud. Math. 126, No. 2, 161--170 (1997; Zbl 0911.46016)].
reviewed by: James V. Whittaker
Mathematics Subject Classification ID: 46E10
zbMATH DE Number: 2136632
zbMATH Keywords: Jackson topology
zbMATH Keywords: dominating norm property
zbMATH Keywords: Whitney functions
zbMATH Keywords: Cantor-type sets
zbMATH Keywords: Markov inequality
author: Muhammed Altun
author: Alexander Goncharov
MaRDI profile type: Publication
full work available at URL: j.jat.2004.10.013
OpenAlex ID: W2164183837
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DOI: 10.1016/J.JAT.2004.10.013
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description: scientific article; zbMATH DE number 2136632