E-Book, Englisch, Band 12, 141 Seiten, eBook
Anandam Harmonic Functions and Potentials on Finite or Infinite Networks
1. Auflage 2011
ISBN: 978-3-642-21399-1
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 12, 141 Seiten, eBook
Reihe: Lecture Notes of the Unione Matematica Italiana
ISBN: 978-3-642-21399-1
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
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.
