Rational approximation to functions like \(x^{\alpha}\) in integral norms
type: Item
instance of: scholarly article
title: Rational approximation to functions like \(x^{\alpha}\) in integral norms
zbMATH Open document ID: 0653.41020
DOI: 10.1007/BF02350637
published in: Analysis Mathematica
publication date: 1988-01-01T00:00:00Z
review text: The main result of the paper concerns the degree of rational approximation in the Hardy space \(H^ p\) of functions that are of Markov-Stieltjes type with special conditions on the measures. As a consequence known estimates for the degree of rational approximation to \(x^{\alpha}\) in \(L^ p[0,1]\), \(1<p<\infty\), for rational \(\alpha\) are extended to hold also for \(\alpha\) irrational. The case when \(\alpha\) is rational was studied by Vjacheslavov and (for \(p=\infty)\) by Ganelius.
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 42B30
zbMATH DE Number: 4065589
zbMATH Keywords: \(H^ p\)-function
zbMATH Keywords: optimal quadrature
zbMATH Keywords: Hahn-Banach theorem
zbMATH Keywords: degree of rational approximation
zbMATH Keywords: Hardy space
author: Jan-Erik Andersson
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02350637
OpenAlex ID: W2314099291
description: scientific article; zbMATH DE number 4065589