Approximation of plurisubharmonic functions on bounded domains in \(\mathbb C^n\)
type: Item
instance of: scholarly article
title: Approximation of plurisubharmonic functions on bounded domains in \(\mathbb C^n\)
zbMATH Open document ID: 1155.32021
published in: Michigan Mathematical Journal
publication date: 2008-11-26T00:00:00Z
review text: Let \(\Omega\) be a domain in \(\mathbb{C}^n\) and \(PSH^- (\Omega)\) be the set of plurisubharmonic functions bounded from above on \(\Omega.\) The main results of this paper are the following facts. {\parindent6mm \begin{itemize}\item[(1)] In Theorem 3.2 it is established when every \(u \in PSH^- (\Omega)\) is the pointwise limit of a sequence \(\{u_j\}\) of smooth plurisubharmonic functions on neighborhood of \(\overline {\Omega}\). Moreover, it is shown that if \(u\) is locally bounded on \(\Omega\), then \(\{u_j\}\) can be chosen such that \[ (d d^c u_j)^n \to (d d^c u)^n \] in the sense of currents. \item[(2)] In Theorem 4.4, a condition for \(\Omega\) so Theorem 3.2 will be valid is given. \end{itemize}}
reviewed by: P. Z. Agranovich
Mathematics Subject Classification ID: 32U05
Mathematics Subject Classification ID: 30D05
zbMATH DE Number: 5373799
zbMATH Keywords: plurisubharmonic function
zbMATH Keywords: Jensen measure
zbMATH Keywords: Monge-Ampere mass
author: Nguyen Quang Dieu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1163789922
OpenAlex ID: W2052368568
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DOI: 10.1307/MMJ/1163789922
description: scientific article; zbMATH DE number 5373799