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OPERATOR THEORETIC ASPECTS OF ERGODIC THEORY IBD

BáLINT FARKAS / MARKUS HAASE / TANJA EISNER
SPRINGER
08 / 2016
9783319371054
Inglés

Sinopse

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:âÇó á an intuitive introduction to ergodic theoryâÇó ááan introduction to the basic notions, constructions, and standard examplesáof topological dynamical systemsâÇó ááKoopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand-Naimark theoremâÇó á measure-preserving dynamical systemsâÇó áávon NeumannâÇÖs Mean Ergodic Theorem and BirkhoffâÇÖs Pointwise Ergodic TheoremâÇó áástrongly and weakly mixing systemsâÇó ááan examination of notions of isomorphism for measure-preserving systemsâÇó ááMarkov operators, and the related concept of a factor of a measure preserving systemâÇó áácompact groups and semigroups, and a powerful tool in their study, the Jacobs-de Leeuw-Glicksberg decompositionâÇó ááan 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, FurstenbergâÇÖs Correspondence Principle, theorems of Roth and Furstenberg-Sárközy)B eyond 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

PVP
51,38€