Inequalities for real-root polynomials and entire functions
type: Item
instance of: scholarly article
title: Inequalities for real-root polynomials and entire functions
zbMATH Open document ID: 1018.33007
DOI: 10.1016/S0196-8858(02)00005-2
author: William H. Foster
author: Ilia Krasikov
published in: Advances in Applied Mathematics
publication date: 2003-03-26T00:00:00Z
review text: The authors study the positivity of the operator \[ \bigcup_{2m} (f)={1\over 2} \sum^{2m}_{j=0} (-1)^{m+j}{2m\choose j} f^{(j)} f^{(2m-j)} \] that generalizes the classical Laguerre operator, and establish some new inequalities where \(\bigcup_{2m}(f)\) is positive for real polynomials with only real roots and for the Laguerre-Pólya class of entire functions. They indicate how their results can be applied to classical orthogonal polynomials. They also make some interesting conjectures about positivity of related operators (on polynomials with only real zeros). There is a comprehensive bibliography.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1888303
zbMATH Keywords: Laguerre-type inequalities
reviewed by: Sanford L. Segal
MaRDI profile type: Publication
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full work available at URL: s0196-8858(02)00005-2
OpenAlex ID: W2007453171
description: scientific article; zbMATH DE number 1888303