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  • Book
  • © 1994

Potential Theory on Infinite Networks

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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
  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

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.

Keywords

  • Infinite Networks
  • Markov chain
  • Potential theory
  • boundary
  • dirichlet
  • discrete potential networks
  • graph theory
  • harmonic analysis
  • combinatorics

Bibliographic Information

  • Book Title: Potential Theory on Infinite Networks

  • Authors: Paolo M. Soardi

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0073995

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Softcover ISBN: 978-3-540-58448-3Published: 26 October 1994

  • eBook ISBN: 978-3-540-48798-2Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 196

  • Topics: Probability Theory, Discrete Mathematics, Potential Theory

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions