Un résultat de division obtenu par les méthodes de l'approximation
type: Item
instance of: scholarly article
title: Un résultat de division obtenu par les méthodes de l'approximation
zbMATH Open document ID: 0549.26012
DOI: 10.1016/0021-9045(84)90010-8
author: Pierre Goetgheluck
published in: Journal of Approximation Theory
publication date: 1984-01-01T00:00:00Z
review text: In this paper, we establish a result of the following type \((\|\cdot \|\) denotes the supremum norm on [-1,1]): Theorem. There exists a constant A such that for any \(g\in C^ p([-1,1])\) satisfying \(g(x)=f(x)| x|^ a\) with f continuous and \(a\in {\mathbb{R}},0<a<p,\) we have either \(\| f\|\leq A\| g\|\) or \(\| f\|\leq A\| g^{(p)}\|^{a/p}\| g\|^{1-a/p}.\) In fact this theorem is proved for g in Lipschitz spaces and satisfying a little more complicated conditions. The proof is done for polynomial functions and extented to other functions by a process of approximation involving Jackson's theorem.
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 3875588
zbMATH Keywords: Kolmogorov inequalities
zbMATH Keywords: division of functions
zbMATH Keywords: Lipschitz spaces
zbMATH Keywords: polynomial functions
zbMATH Keywords: Jackson's theorem
MaRDI profile type: Publication
full work available at URL: 0021-9045(84)90010-8
OpenAlex ID: W2026203657
cites work: Polynomial inequalities and Markov's inequality in weightedL p -spaces
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description: scientific article; zbMATH DE number 3875588