Approximation to subharmonic functions by subharmonic polynomials
type: Item
instance of: scholarly article
title: Approximation to subharmonic functions by subharmonic polynomials
zbMATH Open document ID: 0593.31008
DOI: 10.1007/BF01157680
author: A. S. Shvedov
published in: Mathematical Notes
publication date: 1985-01-01T00:00:00Z
review text: Let D be a domain in \({\mathcal R}^ m\) (m\(\geq 2)\) with connected boundary and let E be a compact subset of D. It is shown that if u is real-valued, continuous and subharmonic in D, then u can be uniformly approximated in E by subharmonic polynomials. This result with ''harmonic'' in place of ''subharmonic'' is a classical theorem of J. L. Walsh. The paper also contains a criterion, in terms of the associated Riesz measure, for a real-valued subharmonic function to be continuous in a domain.
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 3953212
zbMATH Keywords: continuity
zbMATH Keywords: approximation by subharmonic polynomials
zbMATH Keywords: Riesz measure
zbMATH Keywords: subharmonic function
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01157680
OpenAlex ID: W1991207076
description: scientific article; zbMATH DE number 3953212