Harmonic Functions and Potentials on Finite or Infinite Networks

• 1 Laplace Operators on Networks and Trees.- 2 Potential Theory on Finite Networks.- 3 Harmonic Function Theory on Infinite Networks.- 4 Schrödinger Operators and Subordinate Structures on Infinite Networks.- 5 Polyharmonic Functions on Trees.

From the reviews: "In this book a potential-theoretic style of the theory is built into the framework of finite or infinite networks. The motivation of the book is to build a function theory on networks reflecting ideas of potential theory on locally compact spaces. ... The book is written in a reader-friendly way and contains various potential-theoretic results ... ." (Sirkka-Liisa Eriksson, Zentralblatt MATH, Vol. 1239, 2012) "The book under review is a treatise of the potential theory on a network, that is, a graph with edge weights that need not be symmetric. ... Besides being a very useful resource on the current important developments of the subject, this book has the potential even to change the mindset of those who are vocal critics of axiomatic potential theory, which is viewed by some as an abstruse and unappealing field." (Flavia Colonna, Mathematical Reviews, Issue 2012 h)