Potential theory on infinite networks / Paolo M. Soardi
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1590Langue : anglais.Éditeur : Berlin : Springer-Verlag, 1994ISBN: 9783540584483.ISSN: 1617-9692.Sujet MSC : 31C45, Generalizations of potential theory, Other generalizations (nonlinear potential theory, etc.)31C20, Generalizations of potential theory, Discrete potential theory
94C15, Information and communication theory, circuits - Circuits, networks, Applications of graph theory
60J45, Probability theory and stochastic processes - Markov processes, Probabilistic potential theoryEn-ligne : Springerlink | Zentralblatt | MathSciNet
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. (Zentralblatt)
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