A proof of Markov's theorem for polynomials on Banach spaces
type: Item
instance of: scholarly article
title: A proof of Markov's theorem for polynomials on Banach spaces
zbMATH Open document ID: 1194.41043
author: Lawrence A. Harris
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-05-19T00:00:00Z
review text: The author gives an independent proof of the extension of V. A. Markov's theorem to Gâteaux derivatives of arbitrary order for continuous polynomials on any real normed linear space. The proof uses only elementary tools like Lagrange interpolation for the Chebyshev nodes and a Christoffel-Darboux identity for their bivariate analogues.
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 5710093
zbMATH Keywords: normed linear spaces
zbMATH Keywords: Markov inequalities
zbMATH Keywords: bivariate interpolation
zbMATH Keywords: Chebyshev nodes
zbMATH Keywords: Christoffel-Darboux identity
reviewed by: Alexei Lukashov
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.02.050
OpenAlex ID: W2051925412
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DOI: 10.1016/J.JMAA.2010.02.050
description: scientific article; zbMATH DE number 5710093