The eigenstructure of the Bernstein operator
type: Item
instance of: scholarly article
title: The eigenstructure of the Bernstein operator
zbMATH Open document ID: 0963.41006
author: Shaun Cooper
author: Shayne Waldron
published in: Journal of Approximation Theory
publication date: 2001-06-17T00:00:00Z
review text: The authors determine the eigenvalues and eigenfunctions of the Bernstein operator \(B_n\), the latter are, of course, \(n+1\) polynomials of degrees \(k=0,\dots,n\). They show that the \(k\)th eigen-polynomial \(p^{(n)}_k\) has \(k\) simple zeros in \([0,1]\) and describe \(\lim_{n\to\infty}p^{(n)}_k\), for fixed \(k\). Applications are given to iterates of the Bernstein operators, and to Bernstein quasi-interpolants.
reviewed by: D. Leviatan
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 1495767
zbMATH Keywords: eigenvalues and eigenfunctions of the Bernstein operators
MaRDI profile type: Publication
full work available at URL: jath.2000.3464
OpenAlex ID: W2055593645
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DOI: 10.1006/JATH.2000.3464
description: scientific article; zbMATH DE number 1495767