A generalization of Laguerre's theorems on zeros of entire functions
type: Item
instance of: scholarly article
title: A generalization of Laguerre's theorems on zeros of entire functions
zbMATH Open document ID: 0913.30018
DOI: 10.1007/BF02361213
author: S. G. Merzlyakov
published in: Mathematical Notes
publication date: 1999-04-11T00:00:00Z
review text: Let \(f\), \(\varphi\) be entire functions such that \(f\) is of the Laguerre-Pólya class (i.e. \(f\) can be approximated locally uniformly in \(\mathbb C\) by polynomials having only real zeros) and \(\varphi\) is of the form \(\varphi(w)=\exp(aw)\prod_{n=1}^\infty(1+w/w_{n})\exp(-w/w_{n})\), where \(a\in\mathbb R\), \(w_{n}>0\), and \(\sum_{n=1}^\infty w_{n}^{-2}<+\infty\). Put \((Af)(z):=\sum_{n=0}^\infty\varphi(n)\frac{f^{(n)}(0)}{n!}z^{n}\). The author studies relations between zeros of \(f\), \(\varphi\), and \(Af\).
Mathematics Subject Classification ID: 30D15
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 1238027
zbMATH Keywords: entire functions
zbMATH Keywords: Laguerre-Pólya class
reviewed by: Marek Jarnicki
MaRDI profile type: Publication
cites work: AN EXAMPLE IN THE THEORY OF THE SPECTRUM OF A FUNCTION
cites work: Q3848344
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description: scientific article; zbMATH DE number 1238027