Harmonic Functions and Potentials on Finite or Infinite Networks, Paperback / softback Book

Harmonic Functions and Potentials on Finite or Infinite Networks Paperback / softback

Part of the Lecture Notes of the Unione Matematica Italiana series

Description

Random walks, Markov chains and electrical networks serve as an introduction to the study of real-valued functions on finite or infinite graphs, with appropriate interpretations using probability theory and current-voltage laws.

The relation between this type of function theory and the (Newton) potential theory on the Euclidean spaces is well-established.

The latter theory has been variously generalized, one example being the axiomatic potential theory on locally compact spaces developed by Brelot, with later ramifications from Bauer, Constantinescu and Cornea.

A network is a graph with edge-weights that need not be symmetric.

This book presents an autonomous theory of harmonic functions and potentials defined on a finite or infinite network, on the lines of axiomatic potential theory.

Random walks and electrical networks are important sources for the advancement of the theory.

Information

  • Format: Paperback / softback
  • Pages: 141 pages, X, 141 p.
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Publication Date:
  • Category: Complex analysis, complex variables
  • ISBN: 9783642213984

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