Random Fourier Series with Applications to Harmonic Analysis

Marcus, Michael B. & Gilles Pisier

ISBN 10: 0691082898 / ISBN 13: 9780691082899

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

About this Item

"Necessary and sufficient conditions are obtained for the a.s. uniform convergence of random Fourier series on locally compact Abelian groups and on compact non Abelian groups. Many related results such as a central limit theorem are obtained. The methods developed are used to study questions in harmonic analysis which are not intrinsically random." Hardcover, full orange cloth, black titling. Light wear, spine & front cover faded, ink notes & underlining. v, 150 pages, many equations. Size: Octavo.

Seller Inventory # s0303

Bibliographic Details

• Title: Random Fourier Series with Applications to Harmonic Analysis
• Publisher: Princeton University Press / University of Tokyo Press, Princeton
• Publication Date: 1981
• ISBN 10: 0691082898
• ISBN 13: 9780691082899
• Binding: Hard Cover
• Edition: First Edition.
• Condition: Good
• Dust Jacket Condition: No Jacket
• Seller catalogs:
  • Mathematics

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.