Harmonic functions and potentials on finite or infinite networks

Author(s)

• Anandam, Victor

Bibliographic Information

Harmonic functions and potentials on finite or infinite networks

Victor Anandam

（Lecture notes of the Unione matematica italiana, 12）

Springer, c2011

Note

Includes bibliographical references (p. 133-137) and index

"UMI"

Description and Table of Contents

Description

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.

Table of Contents

1 Laplace Operators on Networks and Trees.- 2 Potential Theory on Finite Networks.- 3 Harmonic Function Theory on Infinite Networks.- 4 Schroedinger Operators and Subordinate Structures on Infinite Networks.- 5 Polyharmonic Functions on Trees.

by "Nielsen BookData"

Details

• NCID: BB06321030
• ISBN:
  • 9783642213984
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Berlin
• Pages/Volumes: x, 141 p.
• Size: 24 cm
• Classification:
  • SG : 510
• Parent Bibliography ID:
  • BA78039391