On some zero-increasing operators
type: Item
instance of: scholarly article
title: On some zero-increasing operators
zbMATH Open document ID: 0997.26008
DOI: 10.1023/A:1015618907277
author: J. M. Carnicer
author: J. M. Peña
author: Allan Pinkus
published in: Acta Mathematica Hungarica
publication date: 2002-11-03T00:00:00Z
review text: The paper considers linear operators over coefficients of monovariate polynomials. Applying these operators may alter the number of polynomial zeros (roots) along the real axis. The authors describe the whole set of degree-preserving unit lower triangular linear operators which let the number of real zeros increase for an arbitrary polynomial. This is a generalization of a result of \textit{Pólya} and \textit{Schur} (1914), which was in turn a generalization of a well-known zero-counting theorem by \textit{Laguerre} (1884). The proof relies on the so-called Pólya-Laguerre functions (a special class of entire functions), Hermite polynomials and the Hermite-Poulain theorem.
reviewed by: Didier Henrion
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 30D15
zbMATH DE Number: 1822366
zbMATH Keywords: polynomials
zbMATH Keywords: zero-increasing operators
zbMATH Keywords: Pólya-Laguerre functions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1822366