Operator Theoretic Aspects of Ergodic Theory

Operator Theoretic Aspects of Ergodic Theory
Author :
Publisher : Springer
Total Pages : 630
Release :
ISBN-10 : 9783319168982
ISBN-13 : 3319168983
Rating : 4/5 (983 Downloads)

Book Synopsis Operator Theoretic Aspects of Ergodic Theory by : Tanja Eisner

Download or read book Operator Theoretic Aspects of Ergodic Theory written by Tanja Eisner and published by Springer. This book was released on 2015-11-18 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory. Topics include: • an intuitive introduction to ergodic theory • an introduction to the basic notions, constructions, and standard examples of topological dynamical systems • Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand–Naimark theorem • measure-preserving dynamical systems • von Neumann’s Mean Ergodic Theorem and Birkhoff’s Pointwise Ergodic Theorem • strongly and weakly mixing systems • an examination of notions of isomorphism for measure-preserving systems • Markov operators, and the related concept of a factor of a measure preserving system • compact groups and semigroups, and a powerful tool in their study, the Jacobs–de Leeuw–Glicksberg decomposition • an introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of dynamical systems to combinatorics (theorems of van der Waerden, Gallai,and Hindman, Furstenberg’s Correspondence Principle, theorems of Roth and Furstenberg–Sárközy) Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory


Operator Theoretic Aspects of Ergodic Theory Related Books

Operator Theoretic Aspects of Ergodic Theory
Language: en
Pages: 630
Authors: Tanja Eisner
Categories: Mathematics
Type: BOOK - Published: 2015-11-18 - Publisher: Springer

DOWNLOAD EBOOK

Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the t
Operator Theoretic Aspects of Ergodic Theory
Language: en
Pages:
Authors: Tanja Eisner
Categories:
Type: BOOK - Published: 2015 - Publisher:

DOWNLOAD EBOOK

Stunning recent results by Host-Kra, Green-Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools
An Introduction to Ergodic Theory
Language: en
Pages: 268
Authors: Peter Walters
Categories: Mathematics
Type: BOOK - Published: 2000-10-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

The first part of this introduction to ergodic theory addresses measure-preserving transformations of probability spaces and covers such topics as recurrence pr
Recurrence in Ergodic Theory and Combinatorial Number Theory
Language: en
Pages: 216
Authors: Harry Furstenberg
Categories: Mathematics
Type: BOOK - Published: 2014-07-14 - Publisher: Princeton University Press

DOWNLOAD EBOOK

Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying th
A Course in Operator Theory
Language: en
Pages: 390
Authors: John B. Conway
Categories: Mathematics
Type: BOOK - Published: 2000 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

Operator theory is a significant part of many important areas of modern mathematics: functional analysis, differential equations, index theory, representation t