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Book Harmonic Functions and Potentials on Finite or Infinite Networks (Lecture Notes of the Unione Matematica Italiana)

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Harmonic Functions and Potentials on Finite or Infinite Networks (Lecture Notes of the Unione Matematica Italiana)

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    Available in PDF - DJVU Format | Harmonic Functions and Potentials on Finite or Infinite Networks (Lecture Notes of the Unione Matematica Italiana).pdf | Language: ENGLISH
    Victor Anandam (Author)

    Book details


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.
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Book details

  • PDF | 156 pages
  • Victor Anandam (Author)
  • Springer: 2011 edition (8 July 2011)
  • English
  • 5
  • Science Nature

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