Pointwise Convergence Of Fourier Series On Compact Lie Gropus
Download Pointwise Convergence Of Fourier Series On Compact Lie Gropus full books in PDF, epub, and Kindle. Read online free Pointwise Convergence Of Fourier Series On Compact Lie Gropus ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
On Mean Convergence of Fourier Series on Compact Lie Groups
Author | : Robert Joseph Stanton |
Publisher | : |
Total Pages | : 146 |
Release | : 1974 |
Genre | : Fourier series |
ISBN | : |
Probability on Compact Lie Groups
Author | : David Applebaum |
Publisher | : Springer |
Total Pages | : 236 |
Release | : 2014-06-26 |
Genre | : Mathematics |
ISBN | : 3319078429 |
Probability theory on compact Lie groups deals with the interaction between “chance” and “symmetry,” a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topics presented are: the study of measures via the non-commutative Fourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures and the statistical problem of deconvolution. The emphasis on compact (rather than general) Lie groups helps readers to get acquainted with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance of these groups for applications. The book is primarily aimed at researchers working in probability, stochastic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists, statisticians and engineers who are working on related applications. A background in first year graduate level measure theoretic probability and functional analysis is essential; a background in Lie groups and representation theory is certainly helpful but the first two chapters also offer orientation in these subjects.
On the Pointwise Convergence of Fourier Series
Author | : Charles J. Mozzochi |
Publisher | : Springer |
Total Pages | : 94 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540366563 |
Pointwise Convergence of Fourier Series
Author | : Juan Arias de Reyna |
Publisher | : Springer |
Total Pages | : 180 |
Release | : 2004-10-13 |
Genre | : Mathematics |
ISBN | : 3540458220 |
This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.
Random Fourier Series with Applications to Harmonic Analysis
Author | : Michael B. Marcus |
Publisher | : Princeton University Press |
Total Pages | : 160 |
Release | : 1981-11-21 |
Genre | : Mathematics |
ISBN | : 0691082928 |
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.
Compact Lie Groups
Author | : Mark R. Sepanski |
Publisher | : Springer Science & Business Media |
Total Pages | : 208 |
Release | : 2007-04-05 |
Genre | : Mathematics |
ISBN | : 0387491589 |
Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Coverage includes the construction of the Spin groups, Schur Orthogonality, the Peter-Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and Character Formulas, the Highest Weight Classification, and the Borel-Weil Theorem. The book develops the necessary Lie algebra theory with a streamlined approach focusing on linear Lie groups.
A First Course on Representation Theory and Linear Lie Groups
Author | : S C Bagchi |
Publisher | : Universities Press |
Total Pages | : 110 |
Release | : 2000 |
Genre | : Lie groups |
ISBN | : 9788173712845 |
This book is intended to serve as a textbook for a one-semester course for M.Sc/M.Phil. Students at Indian universities. Students of theoretical physics will also find this exposition useful. The general theory of Lie groups appears formidable to an M.Sc./M.Phil. student.
Fourier Analysis on SU(2)
Author | : Tyler Leaser |
Publisher | : |
Total Pages | : 125 |
Release | : 2012 |
Genre | : Fourier analysis |
ISBN | : |
The set SU(2) of 2x2 unitary matrices with determinant one forms a compact non-abelian Lie group diffeomorphic to the three dimensional sphere. This thesis surveys general theory concerning analysis on compact Lie groups and applies this in the setting of SU(2). Our principal reference is J. Faraut's book {\em Analysis on Lie Groups}. Fundamental results in representation theory with compact Lie groups include the Peter-Weyl Theorem, Plancherel Theorem and a criterion for uniform convergence of Fourier series. On SU(2) we give explicit constructions for Haar measure and all irreducible unitary representations. For purposes of motivation and comparison we also consider analysis on U(1), the unit circle in the complex plane. In this context, the general theory specializes to yield classical results on Fourier series with periodic functions and the heat equation in one dimension. We discuss convergence behavior of Fourier series on SU(2) and show that Cauchy problem for the heat equation with continuous boundary data admits a unique solution.