Complementability of spaces of harmonic functions
type: Item
instance of: scholarly article
title: Complementability of spaces of harmonic functions
zbMATH Open document ID: 1159.46013
author: J. Spurný
published in: Potential Analysis
publication date: 2008-11-25T00:00:00Z
review text: Let \(U\) be a bounded open set in finite dimensions and let \({\mathbf H}(U)\) stand for the space of functions harmonic on \(U\) and continuous on the closure \(\overline U\) of \(U\). The author gives conditions on the set of regular points of \(\overline U\) garanteeing that \({\mathbf H}(U)\) is complemented in \(C({\overline U})\). The proof bases on a thorough analysis of complementarity of a simplicial function space.
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 5373446
zbMATH Keywords: harmonic functions
zbMATH Keywords: complemented subspace, simplex
reviewed by: S. S. Kutateladze
MaRDI profile type: Publication
full work available at URL: s11118-008-9098-0
OpenAlex ID: W2138450870
cites work: Q5611281
cites work: Q4513495
cites work: Q3900495
cites work: Simplicial function spaces and simplexes
cites work: Measure and integration theory. Transl. from the German by Robert B. Burckel
cites work: A predual of \(l_1\) which is not isomorphic to a C(K) space
cites work: Potential theory. An analytic and probabilistic approach to balayage
cites work: Simplicial cones in potential theory
cites work: A simplicial characterization of elliptic harmonic spaces
cites work: Isomorphisms of spaces of continuous affine functions
cites work: Q5662251
cites work: Infinite dimensional convexity.
cites work: Banach spaces whose duals are \(L_ 1\) spaces and their representing matrices
cites work: On approximation of affine Baire-one functions
cites work: Q4146099
cites work: Lectures on Choquet's theorem
cites work: The Dirichlet Problem for Harmonic Functions
cites work: Q4008457
cites work: MEASURABLE SELECTIONS OF REPRESENTING MEASURES
cites work: Opérateurs de Lion, projecteurs boréliens et simplexes analytiques
cites work: Q4440822
cites work: Q4340096
cites work: Representation of abstract affine functions.
cites work: Q4146947
DOI: 10.1007/S11118-008-9098-0
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description: scientific article; zbMATH DE number 5373446