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Operator Theory And Analysis Of Infinite Networks (Hardcover)
Loot Price: R3,816
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Operator Theory And Analysis Of Infinite Networks (Hardcover)
Series: Contemporary Mathematics And Its Applications: Monographs, Expositions And Lecture Notes, 7
Expected to ship within 10 - 15 working days
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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.
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