Topics in Harmonic Analysis and Ergodic Theory

There are strong connections between harmonic analysis and ergodic theory. A recent example of this interaction is the proof of the spectacular result by Terence Tao and Ben Green that the set of prime numbers contains arbitrarily long arithmetic progressions. The breakthrough achieved by Tao and Green is attributed to applications of techniques from ergodic theory and harmonic analysis to problems in number theory. Articles in the present volume are based on talks delivered by plenary speakers at a conference on Harmonic Analysis and Ergodic Theory (DePaul University, Chicago, December 2-4, 2005). Of ten articles, four are devoted to ergodic theory and six to harmonic analysis, although some may fall in either category. The articles are grouped in two parts arranged by topics. Among the topics are ergodic averages, central limit theorems for random walks, Borel foliations, ergodic theory and low pass filters, data fitting using smooth surfaces, Nehari's theorem for a polydisk, uniqueness theorems for multi-dimensional trigonometric series, and Bellman and $s$-functions.In addition to articles on current research topics in harmonic analysis and ergodic theory, this book contains survey articles on convergence problems in ergodic theory and uniqueness problems on multi-dimensional trigonometric series.

Table of Contents:
Topics in ergodic theory and harmonic analysis: An overview by A. I. Zayed The mathematical work of Roger Jones by J. Rosenblatt The central limit theorem for random walks on orbits of probability preserving transformations by Y. Derriennic and M. Lin Probability, ergodic theory, and low-pass filters by R. F. Gundy Ergodic theory on Borel foliations by $\mathbb{R}^n$ and $\mathbb{Z}^n$ by D. J. Rudolph Short review of the work of Professor J. Marshall Ash by G. V. Welland Uniqueness questions for multiple trigonometric series by J. M. Ash and G. Wang Smooth interpolation of functions on $\mathbb{R}^n$ by C. Fefferman Problems in interpolation theory related to the almost everywhere convergence of Fourier series by P. A. Hagelstein Lectures on Nehari's theorem on the polydisk by M. T. Lacey The $s$-function and the exponential integral by L. Slavin and A. Volberg.