Comparison of two capacities in \({\mathbb{C}}^ n\)
type: Item
instance of: scholarly article
title: Comparison of two capacities in \({\mathbb{C}}^ n\)
zbMATH Open document ID: 0576.32029
DOI: 10.1007/BF01174894
author: Herbert J. Alexander
author: B. A. Taylor
published in: Mathematische Zeitschrift
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173456
review text: There exist several different capacities arising naturally in connection with various problems of the theory of holomorphic and plurisubharmonic functions. The relationship between the capacities is far from being clear. In the paper in question a quantitative relationship between the Bedford-Taylor relative capacity and a capacity defined in terms of Tchebycheff constants is established. The result is shown to be connected with the well known Josefson's theorem on the equivalence of locally and globally pluripolar sets in \({\mathbb{C}}^ n\). Also, a short proof of El Mir's extension of Josefson's theorem is given. For related results see \textit{J. Siciak} [''Extremal plurisubharmonic functions and capacities in \({\mathbb{C}}^ n\)''. (1982)] and \textit{N. Levenberg} and \textit{B. A. Taylor} [''Comparison of capacities in \({\mathbb{C}}^ n\)''. Preprint (1983)].
Mathematics Subject Classification ID: 32U05
Mathematics Subject Classification ID: 31C10
Mathematics Subject Classification ID: 32A99
zbMATH DE Number: 3920948
zbMATH Keywords: complex Monge-Ampere operator
zbMATH Keywords: holomorphic functions
zbMATH Keywords: Josefson's
zbMATH Keywords: lemma about normalized polynomials
zbMATH Keywords: plurisubharmonic functions
zbMATH Keywords: Bedford-Taylor relative capacity
zbMATH Keywords: Tchebycheff constants
zbMATH Keywords: pluripolar sets
reviewed by: M. Klimek
MaRDI profile type: Publication
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OpenAlex ID: W2152937551
description: scientific article; zbMATH DE number 3920948