Harmonic Analysis
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Principles Of Harmonic Analysis
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Author : Anton Deitmar
language : en
Publisher: Springer
Release Date : 2014-06-21
Principles Of Harmonic Analysis written by Anton Deitmar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-21 with Mathematics categories.
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.
Harmonic Analysis And Applications
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Author : John J. Benedetto
language : en
Publisher: CRC Press
Release Date : 2020-12-17
Harmonic Analysis And Applications written by John J. Benedetto and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Mathematics categories.
Harmonic analysis plays an essential role in understanding a host of engineering, mathematical, and scientific ideas. In Harmonic Analysis and Applications, the analysis and synthesis of functions in terms of harmonics is presented in such a way as to demonstrate the vitality, power, elegance, usefulness, and the intricacy and simplicity of the subject. This book is about classical harmonic analysis - a textbook suitable for students, and an essay and general reference suitable for mathematicians, physicists, and others who use harmonic analysis. Throughout the book, material is provided for an upper level undergraduate course in harmonic analysis and some of its applications. In addition, the advanced material in Harmonic Analysis and Applications is well-suited for graduate courses. The course is outlined in Prologue I. This course material is excellent, not only for students, but also for scientists, mathematicians, and engineers as a general reference. Chapter 1 covers the Fourier analysis of integrable and square integrable (finite energy) functions on R. Chapter 2 of the text covers distribution theory, emphasizing the theory's useful vantage point for dealing with problems and general concepts from engineering, physics, and mathematics. Chapter 3 deals with Fourier series, including the Fourier analysis of finite and infinite sequences, as well as functions defined on finite intervals. The mathematical presentation, insightful perspectives, and numerous well-chosen examples and exercises in Harmonic Analysis and Applications make this book well worth having in your collection.
An Introduction To Harmonic Analysis
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Author : Yitzhak Katznelson
language : en
Publisher: Cambridge University Press
Release Date : 2004-01-05
An Introduction To Harmonic Analysis written by Yitzhak Katznelson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-05 with Mathematics categories.
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Introduction To Abstract Harmonic Analysis
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Author : Lynn H. Loomis
language : en
Publisher: Courier Corporation
Release Date : 2011-06-01
Introduction To Abstract Harmonic Analysis written by Lynn H. Loomis and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-01 with Mathematics categories.
"Harmonic analysis is a branch of advanced mathematics with applications in such diverse areas as signal processing, medical imaging, and quantum mechanics. This classic monograph is the work of a prominent contributor to the field. Geared toward advanced undergraduates and graduate students, it focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition"--
A Panorama Of Harmonic Analysis
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Author : Steven G. Krantz
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-07-03
A Panorama Of Harmonic Analysis written by Steven G. Krantz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-03 with categories.
A Panorama of Harmonic Analysis treats the subject of harmonic analysis, from its earliest beginnings to the latest research. Following both an historical and a conceptual genesis, the book discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax of the book is a consideration of the earlier ideas from the point of view of spaces of homogeneous type. The book culminates with a discussion of wavelets-one of the newest ideas in the subject. A Panorama of Harmonic Analysis is intended for graduate students, advanced undergraduates, mathematicians, and anyone wanting to get a quick overview of the subject of cummutative harmonic analysis. Applications are to mathematical physics, engineering and other parts of hard science. Required background is calculus, set theory, integration theory, and the theory of sequences and series.
Studies In Harmonic Analysis
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Author : J. Marshall Ash
language : en
Publisher: MAA Press
Release Date : 1976
Studies In Harmonic Analysis written by J. Marshall Ash and has been published by MAA Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Harmonic analysis categories.
Harmonic Analysis
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Author : Henry Helson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Harmonic Analysis written by Henry Helson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
The reader is assumed to know the elementary part of complex funCtion theory, general topology, integration, and linear spaces. All the needed information is contained in a usual first-year graduate course on analysis. These prerequisites are modest but essential. To be sure there is a big gap between learning the Banach-Steinhaus theorem, for example, and applying it to a real problem. Filling that gap is one of the objectives of this book. It is a natural objective, because integration theory and functional analysis to a great extent developed in response to the problems of Fourier series! The exposition has been condensed somewhat by relegating proofs of some technical points to the problem sets. Other problems give results that are needed in subsequent sections; and many problems simply present interesting results of the subject that are not otherwise covered. Problems range in difficulty from very simple to very hard. The system of numeration is simple: Sec. 3. 2 is the second section of Chapter 3. The second section of the current chapter is Sec. 2. Formula (3. 2) is the second formula of Sec. 3, of the current chapter unless otherwise mentioned. With pleasure I record the debt to my notes from a course on Real Variables given by R. Salem in 1945. I wish to thank R. Fefferman, Y. Katznelson, and A. 6 Cairbre for sympathetic criti cism of the manuscript. Mr. Carl Harris of the Addison-Wesley Publishing Company has been most helpful in bringing the book to publication.
Harmonic Analysis
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Author : María Cristina Pereyra
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Harmonic Analysis written by María Cristina Pereyra and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
Conveys the remarkable beauty and applicability of the ideas that have grown from Fourier theory. It presents 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).
The Evolution Of Applied Harmonic Analysis
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Author : Elena Prestini
language : en
Publisher: Birkhäuser
Release Date : 2016-12-01
The Evolution Of Applied Harmonic Analysis written by Elena Prestini and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-01 with Mathematics categories.
A sweeping exploration of the development and far-reaching applications of harmonic analysis such as signal processing, digital music, Fourier optics, radio astronomy, crystallography, medical imaging, spectroscopy, and more. Featuring a wealth of illustrations, examples, and material not found in other harmonic analysis books, this unique monograph skillfully blends together historical narrative with scientific exposition to create a comprehensive yet accessible work. While only an understanding of calculus is required to appreciate it, there are more technical sections that will charm even specialists in harmonic analysis. From undergraduates to professional scientists, engineers, and mathematicians, there is something for everyone here. The second edition of The Evolution of Applied Harmonic Analysis contains a new chapter on atmospheric physics and climate change, making it more relevant for today’s audience. Praise for the first edition: "...can be thoroughly recommended to any reader who is curious about the physical world and the intellectual underpinnings that have lead to our expanding understanding of our physical environment and to our halting steps to control it. Everyone who uses instruments that are based on harmonic analysis will benefit from the clear verbal descriptions that are supplied." — R.N. Bracewell, Stanford University “The book under review is a unique and splendid telling of the triumphs of the fast Fourier transform. I can recommend it unconditionally... Elena Prestini... has taken one major mathematical idea, that of Fourier analysis, and chased down and described a half dozen varied areas in which Fourier analysis and the FFT are now in place. Her book is much to be applauded.” — Society for Industrial and Applied Mathematics “This is not simply a book about mathematics, or even the history of mathematics; it is a story about how the discipline has been applied (to borrow Fourier’s expression) to ‘the public good and the explanation of natural phenomena.’ ... This book constitutes a significant addition to the library of popular mathematical works, and a valuable resource for students of mathematics.” — Mathematical Association of America Reviews
Harmonic Analysis And Applications
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Author : Christopher Heil
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-02
Harmonic Analysis And Applications written by Christopher Heil and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-02 with Mathematics categories.
This self-contained volume in honor of John J. Benedetto covers a wide range of topics in harmonic analysis and related areas. These include weighted-norm inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected are written by prominent researchers and professionals in the field. The book pays tribute to John J. Benedetto’s achievements and expresses an appreciation for the mathematical and personal inspiration he has given to so many students, co-authors, and colleagues.