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.
表中的内容
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.
语言 英语 ● 格式 PDF ● 网页 141 ● ISBN 9783642213991 ● 文件大小 1.6 MB ● 出版者 Springer Berlin ● 市 Heidelberg ● 国家 DE ● 发布时间 2011 ● 下载 24 个月 ● 货币 EUR ● ID 5238895 ● 复制保护 无