00000cmm a22000004a 4500 UP-99796217611212354 Buklod 20230215085534.0 m go j cr |nu|||auu|a 110627s2011 xx u | eng d 9783642213991 (eBook) 3642213995 (eBook) (iLib)UPD-00215704116 DML eng DMLUC QA 405 A53 2011eb Anandam, Victor. Harmonic functions and potentials on finite or infinite networks [electronic resource] Victor Anandam. Berlin New York Springer c2011. 1 online resource (x, 141 p.) Lecture notes of the Unione Matematica Italiana 12. 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. IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. 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. Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink. Harmonic functions. Operator theory. Electronic books. SpringerLink (Online service). Electronic Resource Available for University of the Philippines Diliman via SpringerLink. Click here to access http://link.springer.com/book/10.1007/978-3-642-21399-1 FO Monograph UPD DMLR Electronic Resource