Separate harmonic functions, a Terada-type theorem
type: Item
instance of: scholarly article
title: Separate harmonic functions, a Terada-type theorem
zbMATH Open document ID: 0948.31002
DOI: 10.1023/A:1008656611988
author: Nguyen Thanh Van
published in: Potential Analysis
publication date: 2000-11-08T00:00:00Z
review text: Let \(D\subseteq \mathbb{R}^{m}\) be a domain; \(G\subseteq \mathbb{R}^{n}\) an open set and \(E\subseteq D\) verifying a technical condition analogue of ``local Polya condition of Leja''. It is proved that, if \(f:D\times G \rightarrow C\) is such that: \[ \forall x \in E,\;f(x, \cdot) \text{ is harmonic on } G \] \[ \forall y \in G,\;f(\cdot , y) \text{ is harmonic on } D \] then \(f\) is harmonic on \(D\times G\). The case \(E = D\) was proved by \textit{P. Lelong} [Ann. Inst. Fourier 11, 515-562 (1961; Zbl 0100.07902)].
Mathematics Subject Classification ID: 31B05
zbMATH DE Number: 1436914
zbMATH Keywords: separately harmonic functions
zbMATH Keywords: Hartog's lemma
reviewed by: Liliana Popa
MaRDI profile type: Publication
full work available at URL: a:1008656611988
OpenAlex ID: W2914238861
description: scientific article; zbMATH DE number 1436914