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Lectures on Harmonic Analysis

2003-09-17 Mathematics
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Release : 2003-09-17
Genre : Mathematics
Kind : eBook
Book Rating : 495/5 ( reviews)

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Book Synopsis Lectures on Harmonic Analysis by : Thomas H. Wolff

Download or read book Lectures on Harmonic Analysis written by Thomas H. Wolff. This book was released on 2003-09-17. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. It is both an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture. The usual background material is covered in the first few chapters: the Fourier transform, convolution, the inversion theorem, the uncertainty principle and the method of stationary phase. However, the choice of topics is highly selective, with emphasis on those frequently used in research inspired by the problems discussed in the later chapters. These include questions related to the restriction conjecture and the Kakeya conjecture, distance sets, and Fourier transforms of singular measures. These problems are diverse, but often interconnected; they all combine sophisticated Fourier analysis with intriguing links to other areas of mathematics and they continue to stimulate first-rate work. The book focuses on laying out a solid foundation for further reading and research. Technicalities are kept to a minimum, and simpler but more basic methods are often favored over the most recent methods. The clear style of the exposition and the quick progression from fundamentals to advanced topics ensures that both graduate students and research mathematicians will benefit from the book.

Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis

1994 Mathematics
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Release : 1994
Genre : Mathematics
Kind : eBook
Book Rating : 374/5 ( reviews)

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Book Synopsis Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis by : Hugh L. Montgomery

Download or read book Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis written by Hugh L. Montgomery. This book was released on 1994. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One particularly valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. The book should be a useful resource for harmonic analysts interested in moving into research in analytic number theory. In addition, it is suitable as a textbook in an advanced graduate topics course in number theory.

Harmonic Analysis, Group Representations, Automorphic Forms, and Invariant Theory

2007 Mathematics
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Release : 2007
Genre : Mathematics
Kind : eBook
Book Rating : 798/5 ( reviews)

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Book Synopsis Harmonic Analysis, Group Representations, Automorphic Forms, and Invariant Theory by : Roger Howe

Download or read book Harmonic Analysis, Group Representations, Automorphic Forms, and Invariant Theory written by Roger Howe. This book was released on 2007. Available in PDF, EPUB and Kindle. Book excerpt: This volume carries the same title as that of an international conference held at the National University of Singapore, 9OCo11 January 2006 on the occasion of Roger E. Howe''s 60th birthday. Authored by leading members of the Lie theory community, these contributions, expanded from invited lectures given at the conference, are a fitting tribute to the originality, depth and influence of Howe''s mathematical work. The range and diversity of the topics will appeal to a broad audience of research mathematicians and graduate students interested in symmetry and its profound applications. Sample Chapter(s). Foreword (21 KB). Chapter 1: The Theta Correspondence Over R (342 KB). Contents: The Theta Correspondence over R (J Adams); The Heisenberg Group, SL (3, R), and Rigidity (A iap et al.); Pfaffians and Strategies for Integer Choice Games (R Evans & N Wallach); When is an L -Function Non-Vanishing in Part of the Critical Strip? (S Gelbart); Cohomological Automorphic Forms on Unitary Groups, II: Period Relations and Values of L -Functions (M Harris); The Inversion Formula and Holomorphic Extension of the Minimal Representation of the Conformal Group (T Kobayashi & G Mano); Classification des S(r)ries Discr tes pour Certains Groupes Classiques p- Adiques (C Moeglin); Some Algebras of Essentially Compact Distributions of a Reductive p -Adic Group (A Moy & M Tadic); Annihilators of Generalized Verma Modules of the Scalar Type for Classical Lie Algebras (T Oshima); Branching to a Maximal Compact Subgroup (D A Vogan, Jr.); Small Semisimple Subalgebras of Semisimple Lie Algebras (J F Willenbring & G J Zuckerman). Readership: Graduate students and research mathematicians in harmonic analysis, group representations, automorphic forms and invariant theory."

Representation Discovery Using Harmonic Analysis

2008 Artificial intelligence
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Release : 2008
Genre : Artificial intelligence
Kind : eBook
Book Rating : 590/5 ( reviews)

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Book Synopsis Representation Discovery Using Harmonic Analysis by : Sridhar Mahadevan

Download or read book Representation Discovery Using Harmonic Analysis written by Sridhar Mahadevan. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: "This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particular Fourier and wavelet analysis. A central goal of this book is to show that these analytical tools can be generalized from their usual setting in (infinite-dimensional) Euclidean spaces to discrete (finite-dimensional) spaces typically studied in many subfields of AI. Representation discovery is an actively developing field, and the author hopes this book will encourage other researchers into exploring this exciting area of research."--BOOK JACKET.

Lectures on the Fourier Transform and Its Applications

2019-01-18 Fourier transformations
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Release : 2019-01-18
Genre : Fourier transformations
Kind : eBook
Book Rating : 918/5 ( reviews)

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Book Synopsis Lectures on the Fourier Transform and Its Applications by : Brad G. Osgood

Download or read book Lectures on the Fourier Transform and Its Applications written by Brad G. Osgood. This book was released on 2019-01-18. Available in PDF, EPUB and Kindle. Book excerpt: This book is derived from lecture notes for a course on Fourier analysis for engineering and science students at the advanced undergraduate or beginning graduate level. Beyond teaching specific topics and techniques—all of which are important in many areas of engineering and science—the author's goal is to help engineering and science students cultivate more advanced mathematical know-how and increase confidence in learning and using mathematics, as well as appreciate the coherence of the subject. He promises the readers a little magic on every page. The section headings are all recognizable to mathematicians, but the arrangement and emphasis are directed toward students from other disciplines. The material also serves as a foundation for advanced courses in signal processing and imaging. There are over 200 problems, many of which are oriented to applications, and a number use standard software. An unusual feature for courses meant for engineers is a more detailed and accessible treatment of distributions and the generalized Fourier transform. There is also more coverage of higher-dimensional phenomena than is found in most books at this level.

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