Eventual positivity for analytic functions
type: Item
instance of: scholarly article
title: Eventual positivity for analytic functions
zbMATH Open document ID: 0852.26015
DOI: 10.1007/BF01446297
author: David Handelman
published in: Mathematische Annalen
publication date: 1996-12-04T00:00:00Z
full work available at URL: https://eudml.org/doc/165407
review text: Let \(P\) and \(f\) be real power series with radius of convergence at least one, the former having radius of convergence exactly one and nonnegative coefficients. Under some circumstances (occurring, for example, if the coefficients of \(P\) are bounded above and below by multiples of \(1/(1+ i)^2\) and the absolute values of the coefficients of \(f\) are bounded above by a multiple of their counterparts in \(P\)), we show that \(f\) being strictly positive on the unit interval is sufficient in order that there exists \(n\) such that \(P^n f\) has nonnegative coefficients in its Maclaurin expansion (necessity of the condition is trivial). For other choices of \(P\) the corresponding results may fail, and we investigate how much is still true.
Mathematics Subject Classification ID: 26E05
Mathematics Subject Classification ID: 30B10
Mathematics Subject Classification ID: 26C05
zbMATH DE Number: 861916
zbMATH Keywords: positivity
zbMATH Keywords: real analytic functions
zbMATH Keywords: real power series
zbMATH Keywords: radius of convergence
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 861916