On the uniformity of meromorphic functions
type: Item
instance of: scholarly article
title: On the uniformity of meromorphic functions
zbMATH Open document ID: 0959.46034
author: Nguyen Dinh Lan
published in: Acta Mathematica Vietnamica
publication date: 2001-04-20T00:00:00Z
review text: Let \(E\) and \(F\) be locally convex spaces and \(D\subset E\) open. An \(F\)-valued function \(f\) is said to be meromorphic on \(D\) if it is holomorphic on a dense open subset and is locally the quotient of two holomorphic functions. It is said to be of uniform type if it factors meromorphically through a Banach space. The author gives conditions, in terms of the linear topological invariants, for all meromorphic functions to be of uniform type (\(M=M_u\)): a) If \(E\) is nuclear Fréchet, then \(M(E',F')=M_u(E',F')\) for every Fréchet space \(F\in (LB^\infty)\) if and only if \(E\in (DN)\). b) If \(F\) is Fréchet, then \(M(E',F')=M_u(E',F')\) for every nuclear Fréchet space \(E\in (DN)\) if and only if \(F\in (LB^\infty)\). c) If \(E\) is a Fréchet-Montel space with property \((DN)\) and \(F\) a Fréchet space with property \((\overline{\overline{\Omega}})\), then \(M(E',F')=M_u(E',F')\).
Mathematics Subject Classification ID: 46G20
Mathematics Subject Classification ID: 46A11
Mathematics Subject Classification ID: 32A30
Mathematics Subject Classification ID: 46A04
zbMATH DE Number: 1406565
zbMATH Keywords: meromorphic functions
zbMATH Keywords: uniform type
zbMATH Keywords: locally the quotient of two holomorphic functions
zbMATH Keywords: linear topological invariants
zbMATH Keywords: nuclear Fréchet space
zbMATH Keywords: Fréchet-Montel space
zbMATH Keywords: property \((DN)\)
reviewed by: Ignacio Zalduendo
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1406565