Harmonic functions and potentials on finite or infinite networks

著者

• Anandam, Victor

書誌事項

Harmonic functions and potentials on finite or infinite networks

Victor Anandam

（Lecture notes of the Unione matematica italiana, 12）

Springer, c2011

注記

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

"UMI"

内容説明・目次

内容説明

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.

目次

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.

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詳細情報

• NII書誌ID(NCID): BB06321030
• ISBN:
  • 9783642213984
• 出版国コード: gw
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Berlin
• ページ数/冊数: x, 141 p.
• 大きさ: 24 cm
• 分類:
  • SG : 510
• 親書誌ID:
  • BA78039391