Ergodic Theory And Its Connections With Harmonic Analysis: Proceedings Of The 1993 Alexandria Conference Ergodic Theory And Its Connections With Harmonic Analysis

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. Pointwise Ergodic Theorems Via Harmonic Analysis / Joseph M. Rosenblatt And Mate Wierdl -- Harmonic Analysis In Rigidity Theory / R. J. Spatzier -- Some Properties And Applications Of Joinings In Ergodic Theory / J.-p. Thouvenot -- Ergodic Baker's Transformations / C. J. Bose And P. Grezegorczyk -- Almost Sure Convergence Of Projections To Self-adjoint Operators In L[subscript 2](0,1) / Lech Ciach, Ryszard Jajte And Adam Paskievicz -- Quasi-uniform Limits Of Uniformly Recurrent Points / Tomasz Downarowicz -- Strictly Nonpointwise Markov Operators And Weak Mixing / Tomasz Downarowicz -- Two Techniques In Multiple Recurrence / A. H. Forrest -- For Bernoulli Transformations The Smallest Natural Family Of Factors Consists Of All Factors / Eli Glasner -- Topological Entropy Of Extensions / Eli Glasner And Benjamin Weiss -- Functional Equations Associated With The Spectral Properties Of Compact Group Extensions / Geoffrey Goodson -- Multiple Recurrence For Nilpotent Groups Of Affine Transformations Of The 2-torus / Daniel A. Hendrick -- A Remark On Isometric Extensions In Relatively Independent Joinings / Emmanuel Lesigne -- Three Results In Recurrence / Randall Mccutcheon -- Calculation Of The Limit In The Return Times Theorem For Dunford-schwartz Operators / James H. Olsen -- Eigenfunctions Of T X S And The Conze-lesigne Algebra / Daniel J. Rudolph. Edited By Karl E. Petersen, Ibrahim Salama. Includes Bibliographical References. CONTENTS......Page 5 Preface......Page 7 PART I: SURVEY ARTICLES......Page 9 Pointwise ergodic theorems via harmonic analysis......Page 11 Harmonic analysis in rigidity theory......Page 161 Some properties and applications of joinings in ergodic theory......Page 215 PART II: RESEARCH PAPERS......Page 245 Ergodic baker's transformations......Page 247 Almost sure convergence of projections to self-adjoint operators in L2(0,1)......Page 255 Quasi-uniform limits of uniformly recurrent points......Page 261 Strictly nonpointwise Markov operators and weak mixing......Page 267 Two techniques in multiple recurrence......Page 281 For Bernoulli transformations the smallest natural family of factors consists of all factors......Page 299 Topological entropy of extensions......Page 307 Functional equations associated with the spectral properties of compact group extensions......Page 317 Multiple recurrence for nilpotent groups of affine transformations of the 2-torus......Page 337 A remark on isometric extensions in relatively independent joinings......Page 351 Three results in recurrence......Page 357 Calculation of the limit in the return times theorem for Dunford-Schwartz operators......Page 367 Eigenfunctions of Tx S and the Conze-Lesigne algebra......Page 377 Conference Program......Page 441 List of Participants......Page 443 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. Ergodic theory is a field that is stimulating 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. This book contains survey papers describing the relationship of ergodic theory with convergence, rigidity theory and the theory of joinings. These papers present the background of each area of interaction, the most outstanding results and promising lines of research. They should form perfect starting points for anyone beginning research in one of these areas. Thirteen related research papers describe the work; several treat questions arising from the Furstenberg multiple recurrence theory, while the remainder deal with convergence and a variety of other topics in dynamics. It has been eighty-five years since Bohl [1909], Sierpinski [1910] and Weyl [1910] proved the now famous equidistribution theorem: if a is an irrational number then the sequence a, 2a, 3a . . . is uniformly distributed mod 1. Tutorial survey papers on important areas of ergodic theory, with related research papers