On the Rubel-Taylor problem on a representation of holomorphic functions
type: Item
instance of: scholarly article
title: On the Rubel-Taylor problem on a representation of holomorphic functions
zbMATH Open document ID: 0999.32001
DOI: 10.1023/A:1012343332090
author: B. N. Khabibullin
publication date: 2002-12-02T00:00:00Z
review text: The author studies a problem of the Rubel-Taylor type and gives conditions under which meromorphic functions on \(\mathbb{C}^n\) are represented by the quotient of two entire functions satisfying a certain kind of growth conditions. The problem of this type was studied by \textit{L. A. Rubel} and \textit{B. A. Taylor} [Bull. Soc. Math. Fr. 96, 53-96 (1968; Zbl 0157.39603)] and \textit{J. Miles} [J. Anal. Math. 25, 371-388 (1972; Zbl 0247.30019)] in the case \(n = 1\). To prove the main result, the author extends the notion of Nevanlinna's characteristic function and introduces a class of meromorphic functions on \(\mathbb{C}^n\) satisfying some growth conditions.
reviewed by: Yoshihiro Aihara
Mathematics Subject Classification ID: 32A20
Mathematics Subject Classification ID: 32A22
Mathematics Subject Classification ID: 32A15
zbMATH DE Number: 1729090
zbMATH Keywords: canonical representation
zbMATH Keywords: Rubel-Taylor problem
zbMATH Keywords: meromorphic functions
zbMATH Keywords: quotient of two entire functions
zbMATH Keywords: growth conditions
zbMATH Keywords: Nevanlinna's characteristic function
MaRDI profile type: Publication
full work available at URL: a:1012343332090
OpenAlex ID: W23511376
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1729090