Harmonic Functions and Potentials on Finite or Infinite Networks

• Main Author: Anandam, Victor (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Series: Lecture Notes of the Unione Matematica Italiana, 12
• Subjects: Mathematics.; Functions of complex variables.; Partial differential equations.; Potential theory (Mathematics).; Potential Theory.; Functions of a Complex Variable.; Partial Differential Equations.

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) pote...

Table of Contents:

• 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.