Ergodic Properties of Algebraic Fields, M.S. Keane; Yurij V. Linnik

Автор: Robert M. Gray
Название: Probability, Random Processes, and Ergodic Properties
ISBN: 1489983317 ISBN-13(EAN): 9781489983312
Издательство: Springer
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Цена: 15672.00 р.
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Описание: In this new edition of this classic text, much of the material has been rearranged and revised for pedagogical reasons. Many classic inequalities and proofs are now incorporated into the text, and many citations have been added.

Автор: Furstenberg Harry
Название: Recurrence in Ergodic Theory and Combinatorial Number Theory
ISBN: 0691615365 ISBN-13(EAN): 9780691615363
Издательство: Wiley
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Цена: 6336.00 р.
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Описание: Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make

Автор: Eisner Tanja
Название: Operator Theoretic Aspects of Ergodic Theory
ISBN: 3319168975 ISBN-13(EAN): 9783319168975
Издательство: Springer
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Цена: 9781.00 р.
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Описание: 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-S rk zy)
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

Автор: Viana
Название: Foundations of Ergodic Theory
ISBN: 1107126967 ISBN-13(EAN): 9781107126961
Издательство: Cambridge Academ
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Описание: Rich with examples, applications and over 400 exercises, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. It requires few prerequisites, beginning with elementary material suitable for undergraduate students and gradually building up to more sophisticated topics.