Operator theory and analysis of infinite networks : theory and applications

Author(s)

    • Jørgensen, Palle E. T.
    • Pearse, Erin P. J.

Bibliographic Information

Operator theory and analysis of infinite networks : theory and applications

Palle E.T. Jorgensen, Erin P.J. Pearse

(Contemporary mathematics and its applications : monographs, expositions, and lecture notes, v. 7)

World Scientific, c2023

Available at  / 3 libraries

Search this Book/Journal

Note

Includes bibliographical references and index

Description and Table of Contents

Description

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.

by "Nielsen BookData"

Details

  • NCID
    BD01813098
  • ISBN
    • 9789811265518
  • LCCN
    2022051320
  • Country Code
    us
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    New Jersey
  • Pages/Volumes
    lv, 392 p.
  • Size
    24 cm
  • Parent Bibliography ID
Page Top