Harmonic Functions and Potentials on Finite or Infinite Networks Paperback / softback
Part of the Lecture Notes of the Unione Matematica Italiana series
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.
- Format: Paperback / softback
- Pages: 141 pages, X, 141 p.
- Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Publication Date: 29/06/2011
- Category: Complex analysis, complex variables
- ISBN: 9783642213984
- PDF from £27.19