Harmonic Functions and Potentials on Finite or Infinite Networks

Harmonic Functions and Potentials on Finite or Infinite Networks
Author :
Publisher : Springer Science & Business Media
Total Pages : 152
Release :
ISBN-10 : 9783642213991
ISBN-13 : 3642213995
Rating : 4/5 (995 Downloads)

Book Synopsis Harmonic Functions and Potentials on Finite or Infinite Networks by : Victor Anandam

Download or read book Harmonic Functions and Potentials on Finite or Infinite Networks written by Victor Anandam and published by Springer Science & Business Media. This book was released on 2011-06-27 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


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