Levi extension theorems for meromorphic functions of weak type in infinite dimension
type: Item
instance of: scholarly article
title: Levi extension theorems for meromorphic functions of weak type in infinite dimension
zbMATH Open document ID: 1361.32013
author: Thai Thuan Quang
author: Lien Vuong Lam
published in: Complex Analysis and Operator Theory
publication date: 2017-01-17T00:00:00Z
review text: The authors study Levi type extension problems for meromorphic functions with values in a topological vector space. Let \(F\) be a sequentially complete locally convex space and let \(W\subset F'\) be such that a set \(B\subset F\) is bounded iff \(u(B)\) is bounded for every \(u\in W\). Let \(\Delta\subset\mathbb C\) denote the unit disc and let \(\Delta_r:=r\Delta\). Let \(D\subset\mathbb C^n\) be open and let \(D_\ast\subset D\) be dense in \(D\). Assume that \(f\) is a meromorphic \(F\)-valued function on \(D\times(\Delta_r\setminus\overline\Delta)\) (\(r>1\)) such that for each \(z\in D_\ast\) there exists a set \(P_z\subset\Delta_r\) without accumulation points in \(\Delta_r\) such that for every \(u\in W\) the function \(u(f(z,\cdot))\) has a meromorphic extension to \(\Delta_r\) whose pole set is contained in \(P_z\) and which is locally bounded on \(\Delta_r\setminus P_z\). Then \(f\) extends meromorphically to \(D\times\Delta_r\). The authors discuss also generalizations of the above theorem under weaker assumptions on \(F\) and \(W\).
reviewed by: Marek Jarnicki
Mathematics Subject Classification ID: 32D15
Mathematics Subject Classification ID: 32A20
zbMATH DE Number: 6675406
zbMATH Keywords: meromorphic functions with values in topological vector spaces
zbMATH Keywords: extension of meromorphic functions
MaRDI profile type: Publication
full work available at URL: s11785-016-0548-1
OpenAlex ID: W2341155396
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DOI: 10.1007/S11785-016-0548-1
description: scientific article; zbMATH DE number 6675406