Harmonic functions and potentials on finite or infinite networks
著者
書誌事項
Harmonic functions and potentials on finite or infinite networks
(Lecture notes of the Unione matematica italiana, 12)
Springer, c2011
大学図書館所蔵 件 / 全16件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
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.
「Nielsen BookData」 より