Operator Theory and Analysis of Infinite Networks

Anglický jazyk

Operator Theory and Analysis of Infinite Networks

Vydavateľstvo: World Scientific
Rok vydania: 2023
Formát: Hardback
Rozmer: 235 x 157 mm
Jazyk: Anglický jazyk
ISBN: 9789811265518

Autor: Erin P J Pearse Palle E T Jorgensen

Na objednávku, dodanie 2-4 týždne

143.10 €

bežná cena: 159.00 €

O knihe

This volume considers resistance networks: large graphs which are connected, undirected, and weighted. Such networks provide a discrete model for physical processes in inhomogeneous media, including heat flow through perforated or porous media. These graphs also arise in data science, e.g., considering geometrizations of datasets, statistical inference, or the propagation of memes through social networks. Indeed, network analysis plays a crucial role in many other areas of data science and engineering. In these models, the weights on the edges may be understood as conductances, or as a measure of similarity. Resistance networks also arise in probability, as they correspond to a broad class of Markov chains. The present volume takes the nonstandard approach of analyzing resistance networks from the point of view of Hilbert space theory, where the inner product is defined in terms of Dirichlet energy. The resulting viewpoint emphasizes orthogonality over convexity and provides new insights into the connections between harmonic functions, operators, and boundary theory. Novel applications to mathematical physics are given, especially in regard to the question of self-adjointness of unbounded operators. New topics are covered in a host of areas accessible to multiple audiences, at both beginning and more advanced levels. This is accomplished by directly linking diverse applied questions to such key areas of mathematics as functional analysis, operator theory, harmonic analysis, optimization, approximation theory, and probability theory.