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Author : Yitzhak Katznelson
Publisher :
ISBN 13 :
Total Pages : 292 pages
Book Rating : 4.3/5 (91 download)
Download or read book An Introduction to Harmonic Analysis written by Yitzhak Katznelson and published by . This book was released on 1968 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : María Cristina Pereyra
Publisher : American Mathematical Soc.
ISBN 13 : 0821875663
Total Pages : 410 pages
Book Rating : 4.8/5 (218 download)
Download or read book Harmonic Analysis written by María Cristina Pereyra and published by American Mathematical Soc.. This book was released on 2012 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last 200 years, harmonic analysis has been one of the most influential bodies of mathematical ideas, having been exceptionally significant both in its theoretical implications and in its enormous range of applicability throughout mathematics, science, and engineering. In this book, the authors convey the remarkable beauty and applicability of the ideas that have grown from Fourier theory. They present for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization). While concentrating on the Fourier and Haar cases, the book touches on aspects of the world that lies between these two different ways of decomposing functions: time-frequency analysis (wavelets). Both finite and continuous perspectives are presented, allowing for the introduction of discrete Fourier and Haar transforms and fast algorithms, such as the Fast Fourier Transform (FFT) and its wavelet analogues. The approach combines rigorous proof, inviting motivation, and numerous applications. Over 250 exercises are included in the text. Each chapter ends with ideas for projects in harmonic analysis that students can work on independently. This book is published in cooperation with IAS/Park City Mathematics Institute.
Author : Lynn H. Loomis
Publisher : Courier Corporation
ISBN 13 : 0486282317
Total Pages : 208 pages
Book Rating : 4.4/5 (862 download)
Download or read book Introduction to Abstract Harmonic Analysis written by Lynn H. Loomis and published by Courier Corporation. This book was released on 2013-05-09 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a prominent figure in the field of harmonic analysis, this classic monograph is geared toward advanced undergraduates and graduate students and focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition.
Author : Anton Deitmar
Publisher : Springer Science & Business Media
ISBN 13 : 147573834X
Total Pages : 154 pages
Book Rating : 4.4/5 (757 download)
Download or read book A First Course in Harmonic Analysis written by Anton Deitmar and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : V. S. Varadarajan
Publisher : Cambridge University Press
ISBN 13 : 9780521663625
Total Pages : 326 pages
Book Rating : 4.6/5 (636 download)
Download or read book An Introduction to Harmonic Analysis on Semisimple Lie Groups written by V. S. Varadarajan and published by Cambridge University Press. This book was released on 1999-07-22 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in paperback, this graduate-level textbook is an introduction to the representation theory of semi-simple Lie groups. As such, it will be suitable for research students in algebra and analysis, and for research mathematicians requiring a readable account of the topic. The author emphasizes the development of the central themes of the sunject in the context of special examples, without losing sight of its general flow and structure. The book concludes with appendices sketching some basic topics with a comprehensive guide to further reading.
Author : Yitzhak Katznelson
Publisher : Cambridge University Press
ISBN 13 : 9780521543590
Total Pages : 342 pages
Book Rating : 4.5/5 (435 download)
Download or read book An Introduction to Harmonic Analysis written by Yitzhak Katznelson and published by Cambridge University Press. This book was released on 2004-01-05 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher description
Author : Gerrit van Dijk
Publisher : Walter de Gruyter
ISBN 13 : 3110220202
Total Pages : 234 pages
Book Rating : 4.1/5 (12 download)
Download or read book Introduction to Harmonic Analysis and Generalized Gelfand Pairs written by Gerrit van Dijk and published by Walter de Gruyter. This book was released on 2009-12-23 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as an introduction to harmonic analysis and generalized Gelfand pairs. Starting with the elementary theory of Fourier series and Fourier integrals, the author proceeds to abstract harmonic analysis on locally compact abelian groups and Gelfand pairs. Finally a more advanced theory of generalized Gelfand pairs is developed. This book is aimed at advanced undergraduates or beginning graduate students. The scope of the book is limited, with the aim of enabling students to reach a level suitable for starting PhD research. The main prerequisites for the book are elementary real, complex and functional analysis. In the later chapters, familiarity with some more advanced functional analysis is assumed, in particular with the spectral theory of (unbounded) self-adjoint operators on a Hilbert space. From the contents Fourier series Fourier integrals Locally compact groups Haar measures Harmonic analysis on locally compact abelian groups Theory and examples of Gelfand pairs Theory and examples of generalized Gelfand pairs
Author : Thomas H. Wolff
Publisher : American Mathematical Soc.
ISBN 13 : 0821834495
Total Pages : 154 pages
Book Rating : 4.8/5 (218 download)
Download or read book Lectures on Harmonic Analysis written by Thomas H. Wolff and published by American Mathematical Soc.. This book was released on 2003-09-17 with total page 154 pages. 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.
Author : M. Sugiura
Publisher : Elsevier
ISBN 13 : 9780080887593
Total Pages : 451 pages
Book Rating : 4.8/5 (875 download)
Download or read book Unitary Representations and Harmonic Analysis written by M. Sugiura and published by Elsevier. This book was released on 1990-03-01 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups. The second edition has been brought up to date with a number of textual changes in each of the five chapters, a new appendix on Fatou's theorem has been added in connection with the limits of discrete series, and the bibliography has been tripled in length.
Author : Carlos E. Kenig
Publisher : American Mathematical Soc.
ISBN 13 : 1470461277
Total Pages : 345 pages
Book Rating : 4.4/5 (74 download)
Download or read book Harmonic Analysis and Applications written by Carlos E. Kenig and published by American Mathematical Soc.. This book was released on 2020-12-14 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: The origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric measure theory, number theory, probability, and has countless applications from data analysis to image recognition and from the study of sound and vibrations to the cutting edge of contemporary physics. The present volume is based on lectures presented at the summer school on Harmonic Analysis. These notes give fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field and to senior researchers wishing to keep up with current developments.
Author : Anton Deitmar
Publisher : Springer
ISBN 13 : 3319057928
Total Pages : 332 pages
Book Rating : 4.3/5 (19 download)
Download or read book Principles of Harmonic Analysis written by Anton Deitmar and published by Springer. This book was released on 2014-06-21 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Maurice A. de Gosson
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110722909
Total Pages : 247 pages
Book Rating : 4.1/5 (17 download)
Download or read book Quantum Harmonic Analysis written by Maurice A. de Gosson and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-07-05 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics is arguably one of the most successful scientific theories ever and its applications to chemistry, optics, and information theory are innumerable. This book provides the reader with a rigorous treatment of the main mathematical tools from harmonic analysis which play an essential role in the modern formulation of quantum mechanics. This allows us at the same time to suggest some new ideas and methods, with a special focus on topics such as the Wigner phase space formalism and its applications to the theory of the density operator and its entanglement properties. This book can be used with profit by advanced undergraduate students in mathematics and physics, as well as by confirmed researchers.
Author : Mark A. Pinsky
Publisher : American Mathematical Society
ISBN 13 : 1470475677
Total Pages : 398 pages
Book Rating : 4.4/5 (74 download)
Download or read book Introduction to Fourier Analysis and Wavelets written by Mark A. Pinsky and published by American Mathematical Society. This book was released on 2023-12-21 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concrete introduction to a number of topics in harmonic analysis, accessible at the early graduate level or, in some cases, at an upper undergraduate level. Necessary prerequisites to using the text are rudiments of the Lebesgue measure and integration on the real line. It begins with a thorough treatment of Fourier series on the circle and their applications to approximation theory, probability, and plane geometry (the isoperimetric theorem). Frequently, more than one proof is offered for a given theorem to illustrate the multiplicity of approaches. The second chapter treats the Fourier transform on Euclidean spaces, especially the author's results in the three-dimensional piecewise smooth case, which is distinct from the classical Gibbs–Wilbraham phenomenon of one-dimensional Fourier analysis. The Poisson summation formula treated in Chapter 3 provides an elegant connection between Fourier series on the circle and Fourier transforms on the real line, culminating in Landau's asymptotic formulas for lattice points on a large sphere. Much of modern harmonic analysis is concerned with the behavior of various linear operators on the Lebesgue spaces $L^p(mathbb{R}^n)$. Chapter 4 gives a gentle introduction to these results, using the Riesz–Thorin theorem and the Marcinkiewicz interpolation formula. One of the long-time users of Fourier analysis is probability theory. In Chapter 5 the central limit theorem, iterated log theorem, and Berry–Esseen theorems are developed using the suitable Fourier-analytic tools. The final chapter furnishes a gentle introduction to wavelet theory, depending only on the $L_2$ theory of the Fourier transform (the Plancherel theorem). The basic notions of scale and location parameters demonstrate the flexibility of the wavelet approach to harmonic analysis. The text contains numerous examples and more than 200 exercises, each located in close proximity to the related theoretical material.
Author : Tullio Ceccherini-Silberstein
Publisher : Cambridge University Press
ISBN 13 : 1107182336
Total Pages : 589 pages
Book Rating : 4.1/5 (71 download)
Download or read book Discrete Harmonic Analysis written by Tullio Ceccherini-Silberstein and published by Cambridge University Press. This book was released on 2018-06-21 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.
Author : Gerald B. Folland
Publisher : CRC Press
ISBN 13 : 1498727158
Total Pages : 317 pages
Book Rating : 4.4/5 (987 download)
Download or read book A Course in Abstract Harmonic Analysis written by Gerald B. Folland and published by CRC Press. This book was released on 2016-02-03 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : Hugh L. Montgomery
Publisher : American Mathematical Soc.
ISBN 13 : 0821807374
Total Pages : 242 pages
Book Rating : 4.8/5 (218 download)
Download or read book Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis written by Hugh L. Montgomery and published by American Mathematical Soc.. This book was released on 1994 with total page 242 pages. 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.
Author : Alberto Torchinsky
Publisher : Elsevier
ISBN 13 : 1483268888
Total Pages : 474 pages
Book Rating : 4.4/5 (832 download)
Download or read book Real-Variable Methods in Harmonic Analysis written by Alberto Torchinsky and published by Elsevier. This book was released on 2016-06-03 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
