(DOWNLOAD) "Harmonic Functions and Potentials on Finite or Infinite Networks" by Victor Anandam " eBook PDF Kindle ePub Free
eBook details
- Title: Harmonic Functions and Potentials on Finite or Infinite Networks
- Author : Victor Anandam
- Release Date : January 27, 2011
- Genre: Mathematics,Books,Science & Nature,
- Pages : * pages
- Size : 3484 KB
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.