Operator Theoretic Aspects of Ergodic Theory

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Mathematical Analysis
Cover of the book Operator Theoretic Aspects of Ergodic Theory by Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase ISBN: 9783319168982
Publisher: Springer International Publishing Publication: November 18, 2015
Imprint: Springer Language: English
Author: Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase
ISBN: 9783319168982
Publisher: Springer International Publishing
Publication: November 18, 2015
Imprint: Springer
Language: English

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

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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

More books from Springer International Publishing

Cover of the book The Lysenko Controversy as a Global Phenomenon, Volume 2 by Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase
Cover of the book Ten Laws for Security by Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase
Cover of the book Female Bodies and Sexuality in Iran and the Search for Defiance by Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase
Cover of the book Concise Guide to Computing Foundations by Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase
Cover of the book Chromosomal Translocations and Genome Rearrangements in Cancer by Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase
Cover of the book Building and Using Binoscopes by Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase
Cover of the book Bio-based Polymers and Nanocomposites by Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase
Cover of the book From Cold War to Cyber War by Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase
Cover of the book Approaching the Kannan-Lovász-Simonovits and Variance Conjectures by Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase
Cover of the book Towards the Mathematics of Quantum Field Theory by Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase
Cover of the book Fuzzy Logic in Its 50th Year by Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase
Cover of the book Advances in Production Management Systems. Production Management for Data-Driven, Intelligent, Collaborative, and Sustainable Manufacturing by Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase
Cover of the book Nuclear Fusion with Polarized Fuel by Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase
Cover of the book Migration and Transnationalism Between Switzerland and Bulgaria by Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase
Cover of the book Protest Publics by Tanja Eisner, Bálint Farkas, Rainer Nagel, Markus Haase
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy