Duality of two balayage-space structures and Dirichlet integrals on balayage spaces
type: Item
instance of: scholarly article
title: Duality of two balayage-space structures and Dirichlet integrals on balayage spaces
zbMATH Open document ID: 0840.31013
DOI: 10.1007/BF02345827
author: Fumi-Yuki Maeda
published in: Potential Analysis
publication date: 1996-07-04T00:00:00Z
review text: On munit un espace topologique \(X\), localement compact à base dénombrable, d'une structure \({\mathcal H}\) d'espace de balayage selon \textit{J. Bliedtner} et \textit{H. Hansen} [Potential theory (Universitext, Springer 1986; Zbl 0706.31001)]; à celle-ci on associe une application linéaire \(\sigma\) qui, à chaque élément \(f\) de l'espace vectoriel engendré par les fonctions harmoniques bornées et les potentiels continus bornés, fait correspondre une mesure \(\sigma (f)\) sur \(X\), de manière que \(f\) soit superharmonique sur l'ouvert \(V\) si et seulement si \(\sigma (f) |_V \geq 0\). Les intégrales de Dirichlet sont alors relatives aux mesures \[ \delta_{[f,g]} = f \sigma (g) + g \sigma (f) - \sigma (fg) - fg \sigma (1) \] et \(\delta_f = \delta_{[f,f]}\), celle-ci \(\geq 0\). On peut enfin trouver sur \(X\) une autre structure \(\check {\mathcal H} \) d'espace de balayage, dite en dualité avec \({\mathcal H}\) en ce sens qu'il existe \(\sigma\) et \(\check \sigma\) telles que \(\int f d \check \sigma (\check f) = \int \check f d \sigma (f)\) pour certains couples \((f, \check f)\), et l'on donne 4 façons équivalentes de choisir ces couples.
Mathematics Subject Classification ID: 31D05
zbMATH DE Number: 827491
zbMATH Keywords: balayage space
zbMATH Keywords: Dirichlet integrals
zbMATH Keywords: superharmonic function
reviewed by: Rose-Marie Hervé
MaRDI profile type: Publication
cites work: Potential theory. An analytic and probabilistic approach to balayage
cites work: Duality on harmonic spaces
cites work: Dirichlet integral and energy of potentials on harmonic spaces with adjoint structure
cites work: Martin boundary of a harmonic space with adjoint structure and its applications
cites work: Discrete initial value problems and discrete parabolic potential theory
full work available at URL: https://doi.org/10.1007/bf02345827
OpenAlex ID: W1979005828
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description: scientific article; zbMATH DE number 827491