A Remez-type inequality for non-dense Müntz spaces with explicit bound
type: Item
instance of: scholarly article
title: A Remez-type inequality for non-dense Müntz spaces with explicit bound
zbMATH Open document ID: 0904.41006
author: Peter Borwein
author: Tamás Erdélyi
published in: Journal of Approximation Theory
publication date: 1998-12-29T00:00:00Z
review text: A Remez-type inequality for Müntz polynomials \(p_n(x)=\sum_{k=0}^n a_k x^{\lambda_k}\), or equivalently for Dirichlet sums \(P_n(t)=\sum_{k=0}^n a_k e^{-\lambda_kt}\), is established, where \(\Lambda:=(\lambda_k)_{k=0}^\infty\) denotes a sequence of real numbers satisfying \(0=\lambda_0<\lambda_1<\lambda_2<\ldots\) and \(\sum_{k=1}^\infty 1/\lambda_k<\infty\). An explicit upper bound for a certain constant [discussed in the authors' paper, J. Am. Math. Soc. 10, No. 2, 327-349 (1997; Zbl 0864.41014)] that occurs in the Remez-type inequality is given. In the case \(\lambda_k=k^\alpha\), \(\alpha>1\) it is verified that the bounds are essentially sharp.
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 41A44
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 1197065
zbMATH Keywords: Remez-type inequality
zbMATH Keywords: Müntz spaces
zbMATH Keywords: Dirichlet sums
reviewed by: Nico M. Temme
MaRDI profile type: Publication
full work available at URL: jath.1998.3167
OpenAlex ID: W1990650528
cites work: Generalizations of Müntz’s Theorem via a Remez-type inequality for Müntz spaces
cites work: Q4858543
cites work: Q4340161
cites work: Q3267555
DOI: 10.1006/JATH.1998.3167
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description: scientific article; zbMATH DE number 1197065