Harmonic Functions and Potentials on Finite or Infinite Networks

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...

Full description

Main Author: Anandam, Victor
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2011, 2011
Edition:1st ed. 2011
Series:Lecture Notes of the Unione Matematica Italiana
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
LEADER 02289nmm a2200337 u 4500
001 EB000386962
003 EBX01000000000000000240014
005 00000000000000.0
007 cr|||||||||||||||||||||
008 130626 ||| eng
020 |a 9783642213991 
100 1 |a Anandam, Victor 
245 0 0 |a Harmonic Functions and Potentials on Finite or Infinite Networks  |h Elektronische Ressource  |c by Victor Anandam 
250 |a 1st ed. 2011 
260 |a Berlin, Heidelberg  |b Springer Berlin Heidelberg  |c 2011, 2011 
300 |a X, 141 p  |b online resource 
505 0 |a 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 
653 |a Functions of complex variables 
653 |a Potential theory (Mathematics) 
653 |a Partial Differential Equations 
653 |a Functions of a Complex Variable 
653 |a Partial differential equations 
653 |a Potential Theory 
710 2 |a SpringerLink (Online service) 
041 0 7 |a eng  |2 ISO 639-2 
989 |b Springer  |a Springer eBooks 2005- 
490 0 |a Lecture Notes of the Unione Matematica Italiana 
856 |u https://doi.org/10.1007/978-3-642-21399-1?nosfx=y  |x Verlag  |3 Volltext 
082 0 |a 515.96 
520 |a 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