Operator Theory and Analysis of Infinite Networks
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Operator Theory and Analysis of Infinite Networks

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Operator Theory and Analysis of Infinite NetworksThis 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

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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SKU: 38337654087

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Amazon Customer
Battle Creek, US
★★★★★ 5
Great study book
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Questions are very similar to my current program questions and have great rationales.
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Reviewed in the United States on November 18, 2025
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PTM
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★★★★★ 3
Some errors
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Not too good as I think. Some error between hard copy and online q&a bank. Very careful if you want to study with this
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Reviewed in the United States on August 21, 2025
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Casey Griffiths
Chelsea, US
★★★★★ 1
Poor quality, the book is already falling apart.
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This is a review on quality of the book NOT the content. I just got the book today and the binding on the cover came off immediately. It’s very poorly made!!!
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Reviewed in the United States on May 31, 2026
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2020Shoper
Alexandria, US
★★★★★ 1
Description is misleading
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The description states that the book includes the access code. That is not true, the access code has been used and publisher is not honoring coffee
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Reviewed in the United States on April 24, 2026
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Tab.mariie
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Book as advertised
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Book as advertised
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Reviewed in the United States on March 7, 2026

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