| 书目名称 | Operator Theoretic Aspects of Ergodic Theory | | 编辑 | Tanja Eisner,Bálint Farkas,Rainer Nagel | | 视频video | | | 概述 | Treats both classical and recent results in ergodic theory from a modern analytic perspective.Assumes no background in ergodic theory, while providing a review of basic results in functional analysis. | | 丛书名称 | Graduate Texts in Mathematics | | 图书封面 |  | | 描述 | 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 n | | 出版日期 | Textbook 2015 | | 关键词 | Banach lattices; Jacobs–de Leeuw–Glicksberg Decomposition; Koopman operator; mean ergodic operators; poi | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-16898-2 | | isbn_softcover | 978-3-319-37105-4 | | isbn_ebook | 978-3-319-16898-2Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | Tanja Eisner, B�lint Farkas, Markus Haase, and Rainer Nagel 2015 |
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发表于 2025-3-21 16:43:56
