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＜電子ブック＞
Harmonic Functions and Potentials on Finite or Infinite Networks / by Victor Anandam
(Lecture Notes of the Unione Matematica Italiana. ISSN:18629121 ; 12)

版	1st ed. 2011.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2011
大きさ	X, 141 p : online resource
著者標目	*Anandam, Victor author SpringerLink (Online service)
件　名	LCSH:Potential theory (Mathematics) LCSH:Functions of complex variables LCSH:Differential equations FREE:Potential Theory FREE:Functions of a Complex Variable FREE:Differential Equations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-642-21399-1

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