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Catalogue Information
Field name	Details
Dewey Class	515.96
Title	Harmonic Functions and Potentials on Finite or Infinite Networks (EB) / by Victor Anandam.
Author	Anandam, Victor
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 2011.
Physical Details	X, 141 pages : online resource.
Series	Lecture Notes of the Unione Matematica Italiana 1862-9113 ; ; 12
ISBN	9783642213991
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-642-21399-1
Links to Related Works	Subject References: Differential equations, Partial . Functions of a Complex Variable . Functions of complex variables . Partial differential equations . Potential Theory . Potential theory (Mathematics) . Authors: Anandam, Victor . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes of the Unione Matematica Italiana . Classification: 515.96 .

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Harmonic Functions and Potentials on Finite or Infinite Networks

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