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Topics in Harmonic Analysis and Ergodic Theory
Edited by: Joseph M. Rosenblatt, University of Illinois at Urbana-Champaign, IL, and Alexander M. Stokolos and Ahmed I. Zayed, DePaul University, Chicago, IL
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Contemporary Mathematics
2007; 228 pp; softcover
Volume: 444
ISBN-10: 0-8218-4235-8
ISBN-13: 978-0-8218-4235-5
List Price: US$71
Member Price: US$56.80
Order Code: CONM/444
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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.

Readership

Research mathematicians interested in harmonic analysis, ergodic theory, and their interaction.

Table of Contents

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