Local maximum property and q-plurisubharmonic functions in uniform algebras
type: Item
instance of: scholarly article
title: Local maximum property and q-plurisubharmonic functions in uniform algebras
zbMATH Open document ID: 0646.46047
DOI: 10.1016/0022-247X(86)90027-2
author: Zbigniew Slodkowski
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: There is proven a formula expressing higher order Shilov boundaries of the tensor products of uniform algebras in terms of boundaries of the factor algebras. Main step: Cartesian product of k- and \(\ell\)-maximum sets is a \((k+\ell +1)\)-maximum set. (Definition: locally closed \(X\subset {\mathbb{C}}^ n\) is a k-maximum set if polynomials have local maximum property on intersections of X with (n-k)-dimensional complex planes.) Other properties and characterizations of k-maximum sets are given, e.g., \(X\subset {\mathbb{C}}^ n\) is a k-maximum set iff each k- plurisubharmonic function has local maximum property on X.
Mathematics Subject Classification ID: 46J10
Mathematics Subject Classification ID: 31C10
Mathematics Subject Classification ID: 46M05
zbMATH DE Number: 4054332
zbMATH Keywords: higher order Shilov boundaries
zbMATH Keywords: tensor products of uniform algebras
zbMATH Keywords: boundaries of the factor algebras
zbMATH Keywords: local maximum property
zbMATH Keywords: plurisubharmonic function
MaRDI profile type: Publication
cites work: A Generalized Shilov Boundary and Analytic Structure
cites work: Several dimensional properties of the spectrum of a uniform algebra
cites work: Notions of boundaries for function spaces
cites work: On the conjecture of the equivalence of the plurisubharmonic functions and the Hartogs functions
cites work: Subharmonicity for uniform algebras
cites work: q-plurisubharmonic functions and a generalized Dirichlet problem
cites work: A functionalanalytic characterization of pure-dimensional and regular Stein algebras
cites work: Subharmonic Functions and Uniform Algebras
cites work: Introduction to the theory of analytic spaces
cites work: On the range of an analytic multivalued function
cites work: Analytic phenomena in general function algebras
cites work: Q4125368
cites work: Analytic set-valued functions and spectra
cites work: Q3714379
cites work: Q3708305
cites work: Maximum modulus algebras and singularity sets
description: scientific article; zbMATH DE number 4054332