On some problems concerning holomorphic and plurisubharmonic functions
type: Item
instance of: scholarly article
title: On some problems concerning holomorphic and plurisubharmonic functions
zbMATH Open document ID: 1199.31015
DOI: 10.1007/BF02871851
author: Abidi Jamel
publication date: 2006-04-26T00:00:00Z
review text: Let \(D\) be a domain in \(\mathbb C^n\). The author considers the problem to determine that a function \(f\) is holomorphic (pluriharmonic or \(n\)-harmonic) in \(D\) in terms of some associated function on \(D\times C\). The main results are: (1) \(f\) is holomorphic in \(D\) if and only if \(\log | p(w)-f(z)| \) is plurisubharmonic in \(D\times C\) for some holomorphic polynomial \(p(w)\). (2) \(f\) is pluriharmonic in \(D\) if and only if \(| w-f(z)| \) is plurisubharmonic in \(D\times C\). (3) Two \(n\)-harmonic functions \(f\) and \(g\) in \(D\) are holomorphic in \(D\) if and only if \(\log | w-f(z)| + \log | w-g(z)| \) is plurisubharmonic in \(D\times C\).
Mathematics Subject Classification ID: 31C10
Mathematics Subject Classification ID: 31C05
Mathematics Subject Classification ID: 32U05
zbMATH DE Number: 5019646
zbMATH Keywords: holomorphic functions
zbMATH Keywords: pluriharmonic functions
zbMATH Keywords: plurisubharmonic functions
reviewed by: Lee Taichung
MaRDI profile type: Publication
cites work: Q3852455
cites work: Q5512342
cites work: Q3924489
cites work: Q5586687
cites work: Q4774304
cites work: Q3958740
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full work available at URL: https://doi.org/10.1007/bf02871851
OpenAlex ID: W2022109945
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article