Operator Theory And Analysis Of Infinite Networks
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A01=Erin P J Pearse
A01=Palle Jorgensen
Author_Erin P J Pearse
Author_Palle Jorgensen
Boundaries
Category=PBKB
Discrete Gauss-Green Formulas
Discrete GaussAcAEURA"Green Formulas
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Gaussian Fields and the Malliavin Derivative
Graph Laplacians
Graphs
Harmonic Functions on Networks
Limits of Networks
Machine Learning
Magnetism and Long-Range Order
Optimization
Potentials
Random Walk
Reproducing Kernel Hilbert Spaces
Resistance Boundary
Resistance Metrics
Resistance Network Models
Schoenberg and von Neumann's Embedding Theorem
Selfadjoint
Spectral Theory
Transient Networks
Unbounded Operators
Product details
- ISBN 9789811265518
- Publication Date: 20 Apr 2023
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
