Random Fourier Series with Applications to Harmonic Analysis. (AM-101)

Random Fourier Series with Applications to Harmonic Analysis. (AM-101)

by Michael B. Marcus, Gilles Pisier
     
 

ISBN-10: 0691082928

ISBN-13: 9780691082929

Pub. Date: 11/01/1981

Publisher: Princeton University Press

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

Overview

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.

Product Details

ISBN-13:
9780691082929
Publisher:
Princeton University Press
Publication date:
11/01/1981
Series:
Annals of Mathematics Studies Series, #10
Pages:
152
Product dimensions:
6.05(w) x 9.24(h) x 0.45(d)

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