Harmonic Functions and Potentials on Finite or Infinite Networks

Anandam, Victor

ISBN 10: 3642213987 / ISBN 13: 9783642213984

Published by Springer, 2011

About this Item

Seller Inventory # 12751807-n

Bibliographic Details

• Title: Harmonic Functions and Potentials on Finite or Infinite Networks
• Publisher: Springer
• Publication Date: 2011
• Language: English
• ISBN 10: 3642213987
• ISBN 13: 9783642213984
• Binding: Soft cover
• Condition: New

About this title

Synopsis

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.