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Other titles in the London Mathematical Society Lecture Notes series:
Ergodic Theory and Harmonic Analysis: Proceedings of the 1993 Alexandria Conference (London Mathematical Society Lecture Note)by K. Petersen
Synopses & Reviews
Ergodic theory is a field that is lively on its own and also in its interactions with other branches of mathematics and science. In recent years the interchanges with harmonic analysis have been especially noticeable and productive in both directions. The 1993 Alexandria Conference explored many of these connections as they were developing. The three survey papers in this book describe the relationships of almost everywhere convergence (J. Rosenblatt and M. Wierdl), rigidity theory (R. Spatzier), and the theory of joinings (J.-P. Thouvenot). These papers present the background of each area of interaction, the most outstanding recent results, and the currently promising lines of research. They should form perfect starting points for anyone beginning research in one of these areas. The book also includes thirteen research papers that describe recent work related to the theme of the conference: several treat questions arising from the Furstenberg multiple recurrence theory, while the remainder discuss almost everywhere convergence and a variety of other topics in dynamics.
The papers printed here explore many of the rapidly developing connections between ergodic theory and other branches of mathematics, giving the background of each area, the most outstanding recent results and the most current promising lines of research. They should form perfect starting points for beginning researchers.
This volume contains articles that describe the connections between ergodic theory and convergence, rigidity theory, and the theory of joinings. These papers present the background of each area of interaction, the most outstanding recent results, and the currently promising lines of research. In the aggregate, they will provide a perfect introduction for anyone beginning research in one of these areas.
Tutorial survey papers on important areas of ergodic theory, with related research papers.
Table of Contents
Preface; Part I. Survey Articles: 1. Pointwise ergodic theorems via harmonic analysis Joseph M. Rosenblatt and Máté Wierdl; 2. Harmonic analysis in rigidity theory R. J. Spatzier; 3. Some properties and applications of joinings in ergodic theory J.-P. Thouvenot; Part II. Research Papers: 4. Ergodic baker's transformations C. J. Bose and P. Grezegorczyk; 5. Almost sure convergence of projections to self-adjoint operators in L2(0,1) Lech Ciach, Ryszard Jajte and Adam Paskievicz; 6. Quasi-uniform limits of uniformly recurrent points Tomasz Downarowicz; 7. Strictly nonpointwise Markov operators and weak mixing Tomasz Downarowicz; 8. Two techniques in multiple recurrence A. H. Forrest; 9. For Bernoulli transformations the smallest natural family of factors consists of all factors Eli Glasner; 10. Topological entropy of extensions Eli Glasner and Benjamin Weiss; 11. Functional equations associated with the spectral properties of compact group extensions Geoffrey Goodson; 12. Multiple recurrence for nilpotent groups of affine transformations of the 2-torus Daniel A. Hendrick; 13. A remark on isometric extensions in relatively independent joinings Emmanuel Lesigne; 14. Three results in recurrence Randall McCutcheon; 15. Calculation of the limit in the return times theorem for Dunford-Schwartz operators James H. Olsen; 16. Eigenfunctions of T x S and the Conze-Lesigne algebra Daniel J. Rudolph; Conference program; List of participants.
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