000 02817nam a22004815i 4500
001 978-3-642-21399-1
003 DE-He213
005 20140220083804.0
007 cr nn 008mamaa
008 110627s2011 gw | s |||| 0|eng d
020 _a9783642213991
_9978-3-642-21399-1
024 7 _a10.1007/978-3-642-21399-1
_2doi
050 4 _aQA404.7-405
072 7 _aPBWL
_2bicssc
072 7 _aMAT033000
_2bisacsh
082 0 4 _a515.96
_223
100 1 _aAnandam, Victor.
_eauthor.
245 1 0 _aHarmonic Functions and Potentials on Finite or Infinite Networks
_h[electronic resource] /
_cby Victor Anandam.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2011.
300 _aX, 141p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes of the Unione Matematica Italiana,
_x1862-9113 ;
_v12
505 0 _a1 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.
520 _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.
650 0 _aMathematics.
650 0 _aFunctions of complex variables.
650 0 _aDifferential equations, partial.
650 0 _aPotential theory (Mathematics).
650 1 4 _aMathematics.
650 2 4 _aPotential Theory.
650 2 4 _aFunctions of a Complex Variable.
650 2 4 _aPartial Differential Equations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642213984
830 0 _aLecture Notes of the Unione Matematica Italiana,
_x1862-9113 ;
_v12
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-21399-1
912 _aZDB-2-SMA
999 _c107973
_d107973