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On the Dirichlet problem in the axiomatic theory of harmonic functions
- Source :
- Nagoya Math. J. 23 (1963), 73-96
- Publication Year :
- 1963
- Publisher :
- Duke University Press, 1963.
-
Abstract
- In the frame of the recent axiomatic theories of harmonic functions [2], [3], [1], it has been shown that the continuous bounded functions on the boundaries of relatively compact open sets are resolutive [5], [1]. The aim of the present paper is to substitute in these results the continuous functions by Borel-measurable functions and to leave out the restriction that the open sets are relatively compact. H. Bauer has replaced the axiom 3 of Brelot’s axiomatic by two weaker axioms: the axiom of separation (Trennungsaxiom) and the axiom K1. Since the axiom of separation is not fulfilled in some important cases (e.g. the compact Riemann surfaces) we shall weaken this axiom too, substituting it by one of its consequences: the minimum principle for hyperharmonic functions.
- Subjects :
- Pure mathematics
010308 nuclear & particles physics
General Mathematics
010102 general mathematics
Axiomatic system
Harmonic measure
01 natural sciences
Combinatorics
Mathematics::Logic
symbols.namesake
31.50
Dirichlet eigenvalue
Harmonic function
Relatively compact subspace
Dirichlet's principle
0103 physical sciences
31.20
symbols
Analytic number theory
0101 mathematics
Axiom
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Nagoya Math. J. 23 (1963), 73-96
- Accession number :
- edsair.doi.dedup.....fcd6f26dbdaafa0040558c98beae1813