Universal functions with prescribed zeros and interpolation properties
type: Item
instance of: scholarly article
title: Universal functions with prescribed zeros and interpolation properties
zbMATH Open document ID: 1198.30036
author: A. Bonilla
author: Markus Nieß
author: L. Bernal-González
published in: Michigan Mathematical Journal
publication date: 2010-02-02T00:00:00Z
review text: The authors of this interesting paper study the existence of functions that are \textit{universal} with respect to differential operators and that are, at the same time, ``controlled'' by prescribed interpolation properties, including prescribed zeros and multiplicities. Let \(\Phi(z):=\sum_{n=0}^{\infty}a_nz^n\) denote an entire function of \textit{subexponential type} and consider the infinite-order differential operator \(\Phi(D)\), where \(D=d/dz\). The authors' aim is to prove the existence of holomorphic functions \(f\) on a simply connected domain \(\Omega\) that simultaneously satisfy the following conditions: (a) \(f\) is \(\Phi(D)\)-universal; (b) \(f\) has only zeros at the points of a given subset of \(\Omega\), with prescribed orders; and (c) \(f\) assumes prescribed values at prescribed points (cf. Section 3).
reviewed by: George Csordas
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 47A16
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 30D15
Mathematics Subject Classification ID: 30E05
zbMATH DE Number: 5665437
zbMATH Keywords: universal functions
zbMATH Keywords: infinite-order differential operators
zbMATH Keywords: entire functions of subexponential type
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1260475693
OpenAlex ID: W1965228810
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DOI: 10.1307/MMJ/1260475693
description: scientific article; zbMATH DE number 5665437