Polynomials of best approximation in C[-1,1]
type: Item
instance of: scholarly article
title: Polynomials of best approximation in C[-1,1]
zbMATH Open document ID: 0582.41019
DOI: 10.1007/BF02774085
author: Z. Ditzian
published in: Israel Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: Equivalences between the condition \(| P_ n^{(k)}(x)| \leq K(n^{-1}\sqrt{1-x^ 2}+1/n^ 2)^ kn^{-\alpha},\) where \(P_ n(x)\) is the best n-th degree polynomial approximation to f(x), and the Peetre interpolation space between C[-1,1] and the space \((1-x^ 2)^ kf^{(2k)}(x)\in C[-1,1]\) is established. A similar result is shown for \(E_ n(f)=\inf_{p_ n}\| f-P_ n\|_{C[-1,1]}.\) Rates other than \(n^{-\alpha}\) are also discussed.
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 3931654
zbMATH Keywords: Peetre interpolation space
MaRDI profile type: Publication
cites work: On interpolation of L//p[a,b] and weighted Sobolev spaces
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cites work: Classes de saturation de certains procédés d'approximation des séries de Fourier des fonctions continues et applications à quelques problèmes d'approximation
description: scientific article; zbMATH DE number 3931654