An interpolation characterization of domains of holomorphy
type: Item
instance of: scholarly article
title: An interpolation characterization of domains of holomorphy
zbMATH Open document ID: 0910.32012
DOI: 10.1007/BF02883190
published in: Chinese Science Bulletin
publication date: 1999-04-20T00:00:00Z
review text: The goal of this note is the following: Theorem. Let \(\Omega \subset \mathbb{C}^n\) be a domain. Then \(\Omega\) is a domain of holomorphy if and only if for any sequence of distinct points \(\{p^{(k)}\}^\infty_{k=1} \subset \Omega\) without limit points \(\Omega\), and any sequence of complex numbers \(\{A_k\}^\infty_{k=1}\), there exists a holomorphic function \(f\) in \(\Omega\) such that \(f(p^{(k)}) =A_k\), \(\forall k\in \mathbb{N}\).
Mathematics Subject Classification ID: 32D05
Mathematics Subject Classification ID: 32E30
zbMATH DE Number: 1159082
zbMATH Keywords: interpolation
zbMATH Keywords: analytic sheaf
zbMATH Keywords: domain of holomorphy
author: Taishun Liu
author: Congwen Liu
author: Wenjun Zhang
reviewed by: S. Ivashkovich
MaRDI profile type: Publication
cites work: Q4000467
full work available at URL: https://doi.org/10.1007/bf02883190
OpenAlex ID: W154877312
description: scientific article; zbMATH DE number 1159082