Harmonic Functions and Potentials On Finite Or Infinite Networks.

Anandam Victor

ISBN 10: 3642213987 / ISBN 13: 9783642213984

Editore: Springer, 2011

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Print on Demand pp. x + 141. Codice articolo 3517659

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Titolo: Harmonic Functions and Potentials On Finite ...

Casa editrice: Springer

Data di pubblicazione: 2011

Legatura: Brossura

Condizione: New

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Riassunto:

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.