Trees as Brelot spaces.
type: Item
instance of: scholarly article
title: Trees as Brelot spaces.
zbMATH Open document ID: 1042.31004
DOI: 10.1016/S0196-8858(02)00559-6
author: Joel M. Cohen
author: Flavia Colonna
author: David Singman
author: I. Bajunaid
published in: Advances in Applied Mathematics
publication date: 2003-09-15T00:00:00Z
review text: A Brelot space is a connected locally compact, noncompact Hausdorff space together with the choice of a sheaf of functions on this space, which are called harmonic. The authors prove that by considering functions on a tree to be functions on the edges as well as on the vertices, a tree becomes a Brelot space. This leads to plenty of results on potential theory. By restricting the functions to the vertices only, certain new advances of the potential theory on trees are obtained in the usual sense. This concerns also trees whose nearest-neighbor transition probabilities are defined by both transient and recurrent random walks.
Mathematics Subject Classification ID: 31C20
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 54D45
zbMATH DE Number: 1981416
zbMATH Keywords: harmonic space
zbMATH Keywords: Brelot spaces
zbMATH Keywords: potential theory on trees
reviewed by: Sophia L. Kalpazidou
MaRDI profile type: Publication
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full work available at URL: s0196-8858(02)00559-6
OpenAlex ID: W2015421196
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description: scientific article; zbMATH DE number 1981416