Random Fourier Series with Applications to Harmonic Analysis.

Marcus, Michael B. / Pisier, Gilles.

ISBN 10: 0691082898 / ISBN 13: 9780691082899

Published by Princeton University Press / University of Tokyo Press, Princeton, NJ / Tokyo, 1981

About this Item

24 x 16 cm, hardcover, vi, 150, (2) pages, Text in English, spine sun-faded, no dust jacket, very good condition, see picture. Annals of Mathematics Studies, 101. Advanced monograph on probability theory and harmonic analysis. Develops the theory of random Fourier series and explores its applications in functional analysis and related areas. 360g.

Seller Inventory # 80856

Bibliographic Details

• Title: Random Fourier Series with Applications to Harmonic Analysis.
• Publisher: Princeton University Press / University of Tokyo Press, Princeton, NJ / Tokyo
• Publication Date: 1981
• Language: English
• ISBN 10: 0691082898
• ISBN 13: 9780691082899
• Binding: Hardcover
• Weight: 360 grams
• Seller catalogs:
  • Wetenschap, Techniek

About this title

Synopsis

In this book the authors give the first necessary and sufficient conditions for the uniform convergence a.s. of random Fourier series on locally compact Abelian groups and on compact non-Abelian groups. They also obtain many related results. For example, whenever a random Fourier series converges uniformly a.s. it also satisfies the central limit theorem. The methods developed are used to study some questions in harmonic analysis that are not intrinsically random. For example, a new characterization of Sidon sets is derived.

The major results depend heavily on the Dudley-Fernique necessary and sufficient condition for the continuity of stationary Gaussian processes and on recent work on sums of independent Banach space valued random variables. It is noteworthy that the proofs for the Abelian case immediately extend to the non-Abelian case once the proper definition of random Fourier series is made. In doing this the authors obtain new results on sums of independent random matrices with elements in a Banach space. The final chapter of the book suggests several directions for further research.

From the Back Cover

In a series of three papers published in 1930 and 1931, Paley and Zygmund [44] studied a variety of problems concerning series of independent random functions and raised the question of the uniform convergence a.s. of the random Fourier series.