Harmonic Functions and Potentials on Finite or Infinite Networks

di Victor Anandam (Autore)

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 2011

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.

• Autore: Victor Anandam
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Collana: Lecture Notes of the Unione Matematica Italiana
• Anno: 2011
• Rilegatura: Paperback / softback
• Pagine: 141 p.
• Dimensioni: 235 x 155 mm
• EAN: 9783642213984

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