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About Harmonic Functions and Potentials on Finite or Infinite Networks
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.
Detailed Information
| Author: | Victor Anandam (auth.) |
|---|---|
| Publication Year: | 2011 |
| ISBN: | 9783642213984 |
| Pages: | 153 |
| Language: | English |
| File Size: | 1.099 |
| Format: | |
| Price: | FREE |
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