Markov interlacing property for perfect splines
type: Item
instance of: scholarly article
title: Markov interlacing property for perfect splines
zbMATH Open document ID: 0935.41010
published in: Journal of Approximation Theory
publication date: 1999-12-20T00:00:00Z
review text: The author proves the following generalization of the classical V. A. Markov theorem concerning algebraic polynomials. If the zeros of two perfect splines of a fixed degree interlace, then the zeros of their derivatives also interlace. Recall that a perfect spline of degree \(r\) is an expression of the form \[ p(t):= \sum^r_{j=1} \alpha_j t^{j-1}+ c\Biggl[t^r+ 2 \sum^{n-r}_{i= 1}(-1)^i(t- \xi_i)^r_+\Biggr] \] with real \(\alpha_j\) and \(c_j\) as usual, \(t_+:= \max\{t,0\}\).
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 1356337
zbMATH Keywords: interlacing property
zbMATH Keywords: Chebyshev system
zbMATH Keywords: perfect splines
author: Borislav D. Bojanov
reviewed by: Yuri A. Brudnyi
MaRDI profile type: Publication
full work available at URL: jath.1999.3321
OpenAlex ID: W2087869793
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DOI: 10.1006/JATH.1999.3321
description: scientific article; zbMATH DE number 1356337