Ergodic Theory and Harmonic Analysis: Proceedings of the 1993 Alexandria Conference
Cambridge University Press, Jan 27, 1995 - Mathematics - 437 pages
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.
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PART I SURVEY ARTICLES
PART II RESEARCH PAPERS
Abelian group action algebra automorphism averages bilinear Bourgain C-L extension C-L section cocycle cohomologous commute constant construction Conze-Lesigne Corollary deﬁned Deﬁnition denote discrete disjoint dynamical system eigenfunction element entropy equation ergodic components ergodic dynamical system ergodic theory estimate Example Exercise factor ﬁnd ﬁnite ﬁnite-dimensional ﬁrst ﬁxed Fourier transform function Furstenberg geometric group extension group G harmonic analysis hence horocycle hyperbolic implies inﬁnite invariant inverse limit isomorphic Kazhdan Kronecker lattice Lebesgue Lebesgue measure Lemma Lie groups locally symmetric space manifolds Margulis Math maximal inequality measure-preserving system measure-preserving transformation metric minimal mod q Mostow’s nilpotent group numbers operator order-two pointwise positive integers probability measure probability space proof Proposition prove R. J. Zimmer relatively independent joining result satisﬁes semisimple groups sequence of positive spectral subgroup subset superrigidity Suppose symmetric spaces Theorem topological uniformly recurrent unitary representations universally bad weakly mixing