On the discrete extension of Markov's theorem on monotonicity of zeros
type: Item
instance of: scholarly article
title: On the discrete extension of Markov's theorem on monotonicity of zeros
zbMATH Open document ID: 1333.33013
publication date: 2015-12-15T00:00:00Z
full work available at URL: abstract vol44 pp271-280.html
review text: In 1989 an open problem has been proposed in [\textit{M. E. H. Ismail}, IMA Vol. Math. Appl. 18, 177--190 (1989; Zbl 0698.33008)], concerning the behavior of zeros of orthogonal polynomials associated with a measure given by \(w(x,r)dx+dv(x,r)\), where \(v(.,r)\) is a jump function or a step function. In this article the authors solve a particular case of the open problem, based on the theory of spectral transformations of orthogonal polynomials. Almost at the same period it was also proved in another way in ref. [\textit{D. K. Dimitrov}, ``Monotonicity of zeros of polynomials orthogonal with respect to a discrete measure'', \url{arXiv:1501.07235}].
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 6521227
zbMATH Keywords: orthogonal polynomials on the real line
zbMATH Keywords: Uvarov's transformation
zbMATH Keywords: Markov's theorem
zbMATH Keywords: monotonicity of zeros
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: speed of convergence
author: Kenier Castillo
author: Fernando R. Rafaeli
reviewed by: Chrysoula G. Kokologiannaki
MaRDI profile type: Publication
published in: ETNA - Electronic Transactions on Numerical Analysis
description: scientific article; zbMATH DE number 6521227