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.

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.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1955.

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.

It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research.