Harmonic Functions and Potentials on Finite or Infinite Networks (Lecture Notes of the Unione Matematica Italiana, Band 12) - Softcover

Anandam, Victor

Softcover

ISBN 10: 3642213987 ISBN 13: 9783642213984

Verlag: Springer, 2011

Inhaltsangabe

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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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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2011
• Sprache: Englisch
• ISBN 10: 3642213987
• ISBN 13: 9783642213984
• Einband: Taschenbuch
• Anzahl der Seiten: 156
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