Harmonic Functions and Potentials on Finite or Infinite Networks

By:

Victor Anandam

Format:

Paperback / softback

Series:

Lecture Notes of the Unione Matematica Italiana

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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.

Release date Australia

June 29th, 2011

Author

Victor Anandam

Audience

Professional & Vocational

Illustrations

X, 141 p.

Pages

141

Series

Lecture Notes of the Unione Matematica Italiana

Dimensions

155x235x10

ISBN-13

9783642213984

Product ID

10824794

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