On Mean Convergence of Fourier Series on Compact Lie Groups
Author | : Robert Joseph Stanton |
Publisher | : |
Total Pages | : 146 |
Release | : 1974 |
Genre | : Fourier series |
ISBN | : |
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Author | : Robert Joseph Stanton |
Publisher | : |
Total Pages | : 146 |
Release | : 1974 |
Genre | : Fourier series |
ISBN | : |
Author | : Michael B. Marcus |
Publisher | : Princeton University Press |
Total Pages | : 152 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 1400881536 |
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.
Author | : S.T.L. Choy |
Publisher | : Elsevier |
Total Pages | : 317 |
Release | : 2011-09-22 |
Genre | : Mathematics |
ISBN | : 0080872611 |
The main emphasis of this volume is on harmonic and functional analysis. The papers include some of the latest research developments in this important field of mathematics.
Author | : Dmitriĭ Petrovich Zhelobenko |
Publisher | : American Mathematical Soc. |
Total Pages | : 464 |
Release | : 1973-01-01 |
Genre | : Mathematics |
ISBN | : 9780821886649 |
Author | : Michael B. Marcus |
Publisher | : |
Total Pages | : 150 |
Release | : 1981 |
Genre | : Mathematics |
ISBN | : 9780691082899 |
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.
Author | : Sigurdur Helgason |
Publisher | : American Mathematical Society |
Total Pages | : 667 |
Release | : 2022-03-17 |
Genre | : Mathematics |
ISBN | : 0821832115 |
Group-theoretic methods have taken an increasingly prominent role in analysis. Some of this change has been due to the writings of Sigurdur Helgason. This book is an introduction to such methods on spaces with symmetry given by the action of a Lie group. The introductory chapter is a self-contained account of the analysis on surfaces of constant curvature. Later chapters cover general cases of the Radon transform, spherical functions, invariant operators, compact symmetric spaces and other topics. This book, together with its companion volume, Geometric Analysis on Symmetric Spaces (AMS Mathematical Surveys and Monographs series, vol. 39, 1994), has become the standard text for this approach to geometric analysis. Sigurdur Helgason was awarded the Steele Prize for outstanding mathematical exposition for Groups and Geometric Analysis and Differential Geometry, Lie Groups and Symmetric Spaces.
Author | : Guido Weiss |
Publisher | : American Mathematical Soc. |
Total Pages | : 448 |
Release | : 1979 |
Genre | : Mathematics |
ISBN | : 0821814389 |
Contains sections on Several complex variables, Pseudo differential operators and partial differential equations, Harmonic analysis in other settings: probability, martingales, local fields, and Lie groups and functional analysis.