Separately holomorphic functions on compact sets
type: Item
instance of: scholarly article
title: Separately holomorphic functions on compact sets
zbMATH Open document ID: 0939.32008
author: Nguyen Thai Son
published in: Acta Mathematica Vietnamica
publication date: 2000-01-26T00:00:00Z
review text: Let \(Z\) be a Stein space. Let \({\mathcal H}(Z)\) be the space of holomorphic functions on \(Z\) equipped with the compact-open topology. \({\mathcal H}(Z)\) is said to have the property \[ \text{if }\exists p, \forall q,\;d>0,\;\exists k,\;C>0: \|\cdot\|_q^{1+d}\leq C\|\cdot\|_k \|\cdot \|^d_p. \tag{DN} \] The main aim of the paper is to give a characterization for \({\mathcal H}(Z)\) to have the property (DN) in terms of extension of separately holomorphic functions. It also gives conditions for a compact set \(K\) in a locally irreducible Stein space not to be pluripolar in every irreducible branch of all neighborhoods of \(K\).
reviewed by: Shanyu Ji
Mathematics Subject Classification ID: 32E10
Mathematics Subject Classification ID: 32U05
zbMATH DE Number: 1268013
zbMATH Keywords: separately holomorphic functions
zbMATH Keywords: Stein space
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1268013