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Potential Theory on Infinite Networks

  • Book
  • © 1994

Overview

Authors:
  1. Paolo M. Soardi
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1590)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Kirchhoff's laws

    • Paolo M. Soardi
    Pages 1-21

  3. Finite networks

    • Paolo M. Soardi
    Pages 22-31

  4. Currents and potentials with finite energy

    • Paolo M. Soardi
    Pages 32-71

  5. Uniqueness and related topics

    • Paolo M. Soardi
    Pages 72-99

  6. Some examples and computations

    • Paolo M. Soardi
    Pages 100-130

  7. Royden's compactification

    • Paolo M. Soardi
    Pages 131-159

  8. Rough isometries

    • Paolo M. Soardi
    Pages 160-172

  9. Back Matter

    Pages 173-191
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Keywords

About this book

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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