Duality on harmonic spaces
type: Item
instance of: scholarly article
title: Duality on harmonic spaces
zbMATH Open document ID: 0734.31012
author: Teruo Ikegami
published in: Osaka Journal of Mathematics
publication date: 1991-01-01T00:00:00Z
review text: The following problem from the theory of harmonic spaces is considered. Given a Green function k(x,y), i.e. a system of extremal potentials \(\{k_ y(x)\), \(y\in X\}\) on a harmonic space (X,U), construct a dual harmonic space \((X,U^*)\) such that \(\{k^*_ x(y)=k(x,y)\), \(x\in X\}\) is a system of Green functions on \(U^*\). The problem was solved in the affirmative by Taylor in terms of probability theory. In the present paper a purely potential-theoretic approach is proposed.
Mathematics Subject Classification ID: 31D05
zbMATH DE Number: 4214355
zbMATH Keywords: duality
zbMATH Keywords: harmonic spaces
zbMATH Keywords: Green function
zbMATH Keywords: extremal potentials
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4214355