Potential theory on infinite networks
type: Item
instance of: scholarly article
title: Potential theory on infinite networks
zbMATH Open document ID: 0818.31001
author: Paolo M. Soardi
published in: Lecture Notes in Mathematics
publication date: 1994-11-22T00:00:00Z
review text: The book gives an unified approach to new developments in the theory of infinite networks. Starting by describing and exploring the model of a network and by studying the elementary properties of currents, resistances etc. the note then gives the basic results of infinite networks, existence theorems and Yamasaki's potential theory (restricting the investigation to currents and problems of finite energy). A further chapter is devoted to the problem of uniqueness. After applying the theory to study some particular networks, the Royden compactification of a network along the lines of Royden's compactification for Riemannian manifolds is defined and studied. A final chapter is devoted to rough isometries.
Mathematics Subject Classification ID: 31-02
Mathematics Subject Classification ID: 31C45
Mathematics Subject Classification ID: 94C15
Mathematics Subject Classification ID: 60J45
zbMATH DE Number: 692290
zbMATH Keywords: currents
zbMATH Keywords: resistances
zbMATH Keywords: Yamasaki's potential theory
zbMATH Keywords: uniqueness
zbMATH Keywords: Royden's compactification
zbMATH Keywords: rough isometries
MaRDI profile type: Publication
DOI: 10.1007/BFB0073995
description: scientific article; zbMATH DE number 692290