02275nmm a2200325 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002000139245011300159250001700272260006300289300003000352505025100382653003600633653003500669653002100704653003500725653003500760653003600795710003400831041001900865989003600884490005200920856007200972082001101044520089401055EB000386962EBX0100000000000000024001400000000000000.0cr|||||||||||||||||||||130626 ||| eng a97836422139911 aAnandam, Victor00aHarmonic Functions and Potentials on Finite or Infinite NetworkshElektronische Ressourcecby Victor Anandam a1st ed. 2011 aBerlin, HeidelbergbSpringer Berlin Heidelbergc2011, 2011 aX, 141 pbonline resource0 a1 Laplace Operators on Networks and Trees -- 2 Potential Theory on Finite Networks -- 3 Harmonic Function Theory on Infinite Networks -- 4 SchrÃ¶dinger Operators and Subordinate Structures on Infinite Networks -- 5 Polyharmonic Functions on Trees aDifferential equations, partial aFunctions of complex variables aPotential Theory aPotential theory (Mathematics) aPartial Differential Equations aFunctions of a Complex Variable2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aLecture Notes of the Unione Matematica Italiana uhttps://doi.org/10.1007/978-3-642-21399-1?nosfx=yxVerlag3Volltext0 a515.96 aRandom 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