Potential Theory on Infinite Networks

Paolo M. Soardi (auth.)354058448X, 9783540584483, 354058448X-:, 038758448X

The aim of the book is to give a unified approach to new developments in discrete potential theory and infinite network theory. The author confines himself to the finite energy case, but this does not result in loss of complexity. On the contrary, the functional analytic machinery may be used in analogy with potential theory on Riemann manifolds.
The book is intended for researchers with interdisciplinary interests in one of the following fields: Markov chains, combinatorial graph theory, network theory, Dirichlet spaces, potential theory, abstract harmonic analysis, theory of boundaries.

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Table of contents :
Kirchhoff’s laws….Pages 1-21
Finite networks….Pages 22-31
Currents and potentials withfinite energy….Pages 32-71
Uniqueness and related topics….Pages 72-99
Some examples and computations….Pages 100-130
Royden’s compactification….Pages 131-159
Rough isometries….Pages 160-172