Random Fourier Series with Applications to Harmonic Analysis

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Princeton University Press, 1981 - Mathematics - 150 pages
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The changes to U.S. immigration law that were instituted in 1965 have led to an influx of West African immigrants to New York, creating an enclave Harlem residents now call ''Little Africa.'' These immigrants are immediately recognizable as African in their wide-sleeved robes and tasseled hats, but most native-born members of the community are unaware of the crucial role Islam plays in immigrants' lives. Zain Abdullah takes us inside the lives of these new immigrants and shows how they deal with being a double minority in a country where both blacks and Muslims are stigmatized. Dealing with this dual identity, Abdullah discovers, is extraordinarily complex. Some longtime residents embrace these immigrants and see their arrival as an opportunity to reclaim their African heritage, while others see the immigrants as scornful invaders. In turn, African immigrants often take a particularly harsh view of their new neighbors, buying into the worst stereotypes about American-born blacks being lazy and incorrigible. And while there has long been a large Muslim presence in Harlem, and residents often see Islam as a force for social good, African-born Muslims see their Islamic identity disregarded by most of their neighbors. Abdullah weaves together the stories of these African Muslims to paint a fascinating portrait of a community's efforts to carve out space for itself in a new country. -- Book jacket.
 

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Contents

INTRODUCTION
3
PRELIMINARIES
16
2 A Jensen type inequality for the nondecreasing rearrangement of nonnegative stochastic processes
19
3 Continuity of Gaussian and subGaussian processes
24
4 Sums of Banach space valued random variables
40
RANDOM FOURIER SERIES ON LOCALLY COMPACT ABELIAN GROUPS
51
2 Random Fourier series on the real line
60
3 Random Fourier series on compact Abelian groups
63
3 Continuity of random Fourier series
93
APPLICATIONS TO HARMONIC ANALYSIS
105
2 Applications to Sidon sets
118
ADDITIONAL RESULTS AND COMMENTS
122
2 Almost sure almost periodicity
134
3 On left and right almost sure continuity
138
4 Generalizations
140
REFERENCES
144

THE CENTRAL LIMIT THEOREM AND RELATED QUESTIONS
65
RANDOM FOURIER SERIES ON COMPACT NONABELIAN GROUPS
74
2 Random series with coefficients in a Banach space
81

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Page 145 - Some results on the domain of attraction of stable measures on C(K).
Page 145 - A theorem on the Rademacher series with vector coefficients, Probability in Banach spaces, Lecture Notes in Math.

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About the author (1981)

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Gilles Pisier is Emeritus Professor at the University of Paris VI, where he worked from 1981 to 2010. He is also a Distinguished Professor and holder of the Owen Chair in Mathematics at Texas A&M University. His international prizes include the Salem Prize in harmonic analysis (1979), the Ostrowski Prize (1997), and the Stefan Banach Medal (2001). He is a member of the Paris Academie des Sciences, a Foreign member of the Polish and Indian Academies of Science, and a Fellow of both the IMS and the AMS. He is also the author of several books, notably The Volume of Convex Bodies and Banach Space Geometry (Cambridge, 1989) and Introduction to Operator Space Theory (Cambridge, 2003).

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