Erin P J Pearse's Books

Operator Theory And Analysis Of Infinite Networks

By: Palle Jorgensen,Erin P J Pearse

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Operator Theory And Analysis Of Infinite Networks

By: Palle Jorgensen,Erin P J Pearse

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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449

Publisher

World Scientific

Published Date

ISBN 10

9811265534

ISBN 13

9789811265532

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II

Fractals in Applied Mathematics

By: David Carfi,Michel L. Lapidus,Erin P. J. Pearse,Machiel van Frankenhuijsen

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Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II

Fractals in Applied Mathematics

By: David Carfi,Michel L. Lapidus,Erin P. J. Pearse,Machiel van Frankenhuijsen

This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry and various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry). The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.

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Page Count

384

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821891480

ISBN 13

9780821891483

Operator Theory And Analysis Of Infinite Networks

By: Palle Jorgensen,Erin P J Pearse

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Operator Theory And Analysis Of Infinite Networks

By: Palle Jorgensen,Erin P J Pearse

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

449

Publisher

World Scientific

Published Date

ISBN 10

9811265534

ISBN 13

9789811265532

Book's by Erin P J Pearse

Operator Theory And Analysis Of Infinite Networks

Operator Theory And Analysis Of Infinite Networks

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II

Operator Theory And Analysis Of Infinite Networks

Operator Theory And Analysis Of Infinite Networks

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