Harmonic Functions and Potentials on Finite or Infinite Networks
By: by Victor Anandam
Contributors: SpringerLink (Online service)
Series: Lecture Notes of the Unione Matematica Italiana -- 12
Publisher: Springer-Verlag Berlin Heidelberg
Published: 2011
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 141
ISBN-13: 9783642213984; 9783642213991
Subjects: Potential theory (Mathematics); Mathematics; Functions of complex variables; Partial Differential equations
Description: 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.