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| Author | : Anton Deitmar |
| Publisher | : Springer |
| Total Pages | : 330 |
| Release | : 2014-06-21 |
| Genre | : Mathematics |
| ISBN | : 3319057928 |
Download Principles of Harmonic Analysis Book in PDF, ePub and Kindle
This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.
| Author | : Walter Piston |
| Publisher | : |
| Total Pages | : 90 |
| Release | : 1960 |
| Genre | : |
| ISBN | : |
Download Principles of Harmonic Analysis Book in PDF, ePub and Kindle
| Author | : Anton Deitmar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 154 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 147573834X |
Download A First Course in Harmonic Analysis Book in PDF, ePub and Kindle
This book introduces harmonic analysis at an undergraduate level. In doing so it covers Fourier analysis and paves the way for Poisson Summation Formula. Another central feature is that is makes the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The final goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.
| Author | : Victor Havin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 547 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642783775 |
Download The Uncertainty Principle in Harmonic Analysis Book in PDF, ePub and Kindle
The present book is a collection of variations on a theme which can be summed up as follows: It is impossible for a non-zero function and its Fourier transform to be simultaneously very small. In other words, the approximate equalities x :::::: y and x :::::: fj cannot hold, at the same time and with a high degree of accuracy, unless the functions x and yare identical. Any information gained about x (in the form of a good approximation y) has to be paid for by a corresponding loss of control on x, and vice versa. Such is, roughly speaking, the import of the Uncertainty Principle (or UP for short) referred to in the title ofthis book. That principle has an unmistakable kinship with its namesake in physics - Heisenberg's famous Uncertainty Principle - and may indeed be regarded as providing one of mathematical interpretations for the latter. But we mention these links with Quantum Mechanics and other connections with physics and engineering only for their inspirational value, and hasten to reassure the reader that at no point in this book will he be led beyond the world of purely mathematical facts. Actually, the portion of this world charted in our book is sufficiently vast, even though we confine ourselves to trigonometric Fourier series and integrals (so that "The U. P. in Fourier Analysis" might be a slightly more appropriate title than the one we chose).
| Author | : Alberto Torchinsky |
| Publisher | : Elsevier |
| Total Pages | : 475 |
| Release | : 2016-06-03 |
| Genre | : Mathematics |
| ISBN | : 1483268888 |
Download Real-Variable Methods in Harmonic Analysis Book in PDF, ePub and Kindle
Real-Variable Methods in Harmonic Analysis deals with the unity of several areas in harmonic analysis, with emphasis on real-variable methods. Active areas of research in this field are discussed, from the Calderón-Zygmund theory of singular integral operators to the Muckenhoupt theory of Ap weights and the Burkholder-Gundy theory of good ? inequalities. The Calderón theory of commutators is also considered. Comprised of 17 chapters, this volume begins with an introduction to the pointwise convergence of Fourier series of functions, followed by an analysis of Cesàro summability. The discussion then turns to norm convergence; the basic working principles of harmonic analysis, centered around the Calderón-Zygmund decomposition of locally integrable functions; and fractional integration. Subsequent chapters deal with harmonic and subharmonic functions; oscillation of functions; the Muckenhoupt theory of Ap weights; and elliptic equations in divergence form. The book also explores the essentials of the Calderón-Zygmund theory of singular integral operators; the good ? inequalities of Burkholder-Gundy; the Fefferman-Stein theory of Hardy spaces of several real variables; Carleson measures; and Cauchy integrals on Lipschitz curves. The final chapter presents the solution to the Dirichlet and Neumann problems on C1-domains by means of the layer potential methods. This monograph is intended for graduate students with varied backgrounds and interests, ranging from operator theory to partial differential equations.
| Author | : Joseph Albert Wolf |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 408 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821842897 |
Download Harmonic Analysis on Commutative Spaces Book in PDF, ePub and Kindle
This study starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces.
| Author | : Roger Howe |
| Publisher | : World Scientific |
| Total Pages | : 446 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 9812770798 |
Download Harmonic Analysis, Group Representations, Automorphic Forms, and Invariant Theory Book in PDF, ePub and Kindle
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."
| Author | : Hugo D. Junghenn |
| Publisher | : CRC Press |
| Total Pages | : 520 |
| Release | : 2018-04-27 |
| Genre | : Mathematics |
| ISBN | : 149877329X |
Download Principles of Analysis Book in PDF, ePub and Kindle
Principles of Analysis: Measure, Integration, Functional Analysis, and Applications prepares readers for advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level. The book also helps them prepare for qualifying exams in real analysis. It is designed so that the reader or instructor may select topics suitable to their needs. The author presents the text in a clear and straightforward manner for the readers’ benefit. At the same time, the text is a thorough and rigorous examination of the essentials of measure, integration and functional analysis. The book includes a wide variety of detailed topics and serves as a valuable reference and as an efficient and streamlined examination of advanced real analysis. The text is divided into four distinct sections: Part I develops the general theory of Lebesgue integration; Part II is organized as a course in functional analysis; Part III discusses various advanced topics, building on material covered in the previous parts; Part IV includes two appendices with proofs of the change of the variable theorem and a joint continuity theorem. Additionally, the theory of metric spaces and of general topological spaces are covered in detail in a preliminary chapter . Features: Contains direct and concise proofs with attention to detail Features a substantial variety of interesting and nontrivial examples Includes nearly 700 exercises ranging from routine to challenging with hints for the more difficult exercises Provides an eclectic set of special topics and applications About the Author: Hugo D. Junghenn is a professor of mathematics at The George Washington University. He has published numerous journal articles and is the author of several books, including Option Valuation: A First Course in Financial Mathematics and A Course in Real Analysis. His research interests include functional analysis, semigroups, and probability.
| Author | : Walter Piston |
| Publisher | : Boston : E.C. Schirmer |
| Total Pages | : 108 |
| Release | : 1933 |
| Genre | : Music |
| ISBN | : |
Download Principles of Harmonic Analysis Book in PDF, ePub and Kindle
| Author | : Gerald B. Folland |
| Publisher | : CRC Press |
| Total Pages | : 317 |
| Release | : 2016-02-03 |
| Genre | : Mathematics |
| ISBN | : 1498727158 |
Download A Course in Abstract Harmonic Analysis Book in PDF, ePub and Kindle
A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul
