Fourier Analysis

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Classical Fourier Analysis

Loukas Grafakos
Classical Fourier Analysis Book PDF

Author : Loukas Grafakos
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 41,8 Mb
Release : 2008-09-18
Category : Mathematics
ISBN : 9780387094328

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Classical Fourier Analysis by Loukas Grafakos Pdf

The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. This book is mainly addressed to graduate students in mathematics and is designed to serve for a three-course sequence on the subject. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration, and complex variables. This book is intended to present the selected topics in some depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables. While the 1st edition was published as a single volume, the new edition will contain 120 pp of new material, with an additional chapter on time-frequency analysis and other modern topics. As a result, the book is now being published in 2 separate volumes, the first volume containing the classical topics (Lp Spaces, Littlewood-Paley Theory, Smoothness, etc...), the second volume containing the modern topics (weighted inequalities, wavelets, atomic decomposition, etc...). From a review of the first edition: “Grafakos’s book is very user-friendly with numerous examples illustrating the definitions and ideas. It is more suitable for readers who want to get a feel for current research. The treatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises.” - Ken Ross, MAA Online

Data-Driven Science and Engineering

Steven L. Brunton,J. Nathan Kutz
Data Driven Science and Engineering Book PDF

Author : Steven L. Brunton,J. Nathan Kutz
Publisher : Cambridge University Press
Page : 615 pages
File Size : 47,7 Mb
Release : 2022-05-05
Category : Computers
ISBN : 9781009098489

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Data-Driven Science and Engineering by Steven L. Brunton,J. Nathan Kutz Pdf

A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.

Numerical Fourier Analysis

Gerlind Plonka,Daniel Potts,Gabriele Steidl,Manfred Tasche
Numerical Fourier Analysis Book PDF

Author : Gerlind Plonka,Daniel Potts,Gabriele Steidl,Manfred Tasche
Publisher : Springer
Page : 618 pages
File Size : 44,9 Mb
Release : 2019-02-05
Category : Mathematics
ISBN : 9783030043063

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Numerical Fourier Analysis by Gerlind Plonka,Daniel Potts,Gabriele Steidl,Manfred Tasche Pdf

This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods. It starts with a detailed discussion of classical Fourier theory to enable readers to grasp the construction and analysis of advanced fast Fourier algorithms introduced in the second part, such as nonequispaced and sparse FFTs in higher dimensions. Lastly, it contains a selection of numerical applications, including recent research results on nonlinear function approximation by exponential sums. The code of most of the presented algorithms is available in the authors’ public domain software packages. Students and researchers alike benefit from this unified presentation of Fourier theory and corresponding algorithms.

Fourier Analysis in Several Complex Variables

Leon Ehrenpreis
Fourier Analysis in Several Complex Variables Book PDF

Author : Leon Ehrenpreis
Publisher : Courier Corporation
Page : 532 pages
File Size : 55,5 Mb
Release : 2011-11-30
Category : Mathematics
ISBN : 9780486153032

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Fourier Analysis in Several Complex Variables by Leon Ehrenpreis Pdf

Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations. 1970 edition.

Applied Fourier Analysis

Tim Olson
Applied Fourier Analysis Book PDF

Author : Tim Olson
Publisher : Birkhäuser
Page : 302 pages
File Size : 45,6 Mb
Release : 2017-11-20
Category : Mathematics
ISBN : 9781493973934

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Applied Fourier Analysis by Tim Olson Pdf

The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing. Developed by the author from extensive classroom teaching experience, it provides a breadth of theory that allows students to appreciate the utility of the subject, but at as accessible a depth as possible. With myriad applications included, this book can be adapted to a one or two semester course in Fourier Analysis or serve as the basis for independent study. Applied Fourier Analysis assumes no prior knowledge of analysis from its readers, and begins by making the transition from linear algebra to functional analysis. It goes on to cover basic Fourier series and Fourier transforms before delving into applications in sampling and interpolation theory, digital communications, radar processing, medi cal imaging, and heat and wave equations. For all applications, ample practice exercises are given throughout, with collections of more in-depth problems built up into exploratory chapter projects. Illuminating videos are available on Springer.com and Link.Springer.com that present animated visualizations of several concepts. The content of the book itself is limited to what students will need to deal with in these fields, and avoids spending undue time studying proofs or building toward more abstract concepts. The book is perhaps best suited for courses aimed at upper division undergraduates and early graduates in mathematics, electrical engineering, mechanical engineering, computer science, physics, and other natural sciences, but in general it is a highly valuable resource for introducing a broad range of students to Fourier analysis.

Fourier Analysis on Finite Groups and Applications

Audrey Terras
Fourier Analysis on Finite Groups and Applications Book PDF

Author : Audrey Terras
Publisher : Cambridge University Press
Page : 456 pages
File Size : 50,9 Mb
Release : 1999-03-28
Category : Mathematics
ISBN : 0521457181

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Fourier Analysis on Finite Groups and Applications by Audrey Terras Pdf

It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research.

Fourier Analysis

T. W. Körner
Fourier Analysis Book PDF

Author : T. W. Körner
Publisher : Cambridge University Press
Page : 128 pages
File Size : 43,9 Mb
Release : 2022-06-09
Category : Mathematics
ISBN : 9781009230070

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Fourier Analysis by T. W. Körner Pdf

Fourier analysis is a subject that was born in physics but grew up in mathematics. Now it is part of the standard repertoire for mathematicians, physicists and engineers. This diversity of interest is often overlooked, but in this much-loved book, Tom Körner provides a shop window for some of the ideas, techniques and elegant results of Fourier analysis, and for their applications. These range from number theory, numerical analysis, control theory and statistics, to earth science, astronomy and electrical engineering. The prerequisites are few (a reader with knowledge of second- or third-year undergraduate mathematics should have no difficulty following the text), and the style is lively and entertaining. This edition of Körner's 1989 text includes a foreword written by Professor Terence Tao introducing it to a new generation of fans.

An Introduction to Fourier Analysis

Russell L. Herman
An Introduction to Fourier Analysis Book PDF

Author : Russell L. Herman
Publisher : CRC Press
Page : 527 pages
File Size : 49,6 Mb
Release : 2016-09-19
Category : Mathematics
ISBN : 9781498773720

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An Introduction to Fourier Analysis by Russell L. Herman Pdf

This book helps students explore Fourier analysis and its related topics, helping them appreciate why it pervades many fields of mathematics, science, and engineering. This introductory textbook was written with mathematics, science, and engineering students with a background in calculus and basic linear algebra in mind. It can be used as a textbook for undergraduate courses in Fourier analysis or applied mathematics, which cover Fourier series, orthogonal functions, Fourier and Laplace transforms, and an introduction to complex variables. These topics are tied together by the application of the spectral analysis of analog and discrete signals, and provide an introduction to the discrete Fourier transform. A number of examples and exercises are provided including implementations of Maple, MATLAB, and Python for computing series expansions and transforms. After reading this book, students will be familiar with: • Convergence and summation of infinite series • Representation of functions by infinite series • Trigonometric and Generalized Fourier series • Legendre, Bessel, gamma, and delta functions • Complex numbers and functions • Analytic functions and integration in the complex plane • Fourier and Laplace transforms. • The relationship between analog and digital signals Dr. Russell L. Herman is a professor of Mathematics and Professor of Physics at the University of North Carolina Wilmington. A recipient of several teaching awards, he has taught introductory through graduate courses in several areas including applied mathematics, partial differential equations, mathematical physics, quantum theory, optics, cosmology, and general relativity. His research interests include topics in nonlinear wave equations, soliton perturbation theory, fluid dynamics, relativity, chaos and dynamical systems.

Fourier Analysis on Number Fields

Dinakar Ramakrishnan,Robert J. Valenza
Fourier Analysis on Number Fields Book PDF

Author : Dinakar Ramakrishnan,Robert J. Valenza
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 43,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475730852

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Fourier Analysis on Number Fields by Dinakar Ramakrishnan,Robert J. Valenza Pdf

A modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasising harmonic analysis on topological groups. The main goal is to cover John Tates visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries -- technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist. While most of the existing treatments of Tates thesis are somewhat terse and less than complete, the intent here is to be more leisurely, more comprehensive, and more comprehensible. While the choice of objects and methods is naturally guided by specific mathematical goals, the approach is by no means narrow. In fact, the subject matter at hand is germane not only to budding number theorists, but also to students of harmonic analysis or the representation theory of Lie groups. The text addresses students who have taken a year of graduate-level course in algebra, analysis, and topology. Moreover, the work will act as a good reference for working mathematicians interested in any of these fields.

Discrete Fourier Analysis

M. W. Wong
Discrete Fourier Analysis Book PDF

Author : M. W. Wong
Publisher : Springer Science & Business Media
Page : 177 pages
File Size : 41,5 Mb
Release : 2011-05-30
Category : Mathematics
ISBN : 9783034801164

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Discrete Fourier Analysis by M. W. Wong Pdf

This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis. The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis. Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study.

Fourier Analysis and Its Applications

Anders Vretblad
Fourier Analysis and Its Applications Book PDF

Author : Anders Vretblad
Publisher : Springer Science & Business Media
Page : 275 pages
File Size : 46,9 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387217239

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Fourier Analysis and Its Applications by Anders Vretblad Pdf

A carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral. Readers should be familiar with calculus, linear algebra, and complex numbers. At the same time, the author has managed to include discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually does not find in books at this level. A variety of worked examples and exercises will help the readers to apply their newly acquired knowledge.

Fourier Analysis

Elias M. Stein,Rami Shakarchi
Fourier Analysis Book PDF

Author : Elias M. Stein,Rami Shakarchi
Publisher : Princeton University Press
Page : 326 pages
File Size : 54,5 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 9781400831234

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Fourier Analysis by Elias M. Stein,Rami Shakarchi Pdf

This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Fourier Analysis

Javier Duoandikoetxea Zuazo
Fourier Analysis Book PDF

Author : Javier Duoandikoetxea Zuazo
Publisher : American Mathematical Soc.
Page : 248 pages
File Size : 41,9 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 0821883844

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Fourier Analysis by Javier Duoandikoetxea Zuazo Pdf

Fourier analysis encompasses a variety of perspectives and techniques. This volume presents the real variable methods of Fourier analysis introduced by Calderón and Zygmund. The text was born from a graduate course taught at the Universidad Autonoma de Madrid and incorporates lecture notes from a course taught by José Luis Rubio de Francia at the same university. Motivated by the study of Fourier series and integrals, classical topics are introduced, such as the Hardy-Littlewood maximal function and the Hilbert transform. The remaining portions of the text are devoted to the study of singular integral operators and multipliers. Both classical aspects of the theory and more recent developments, such as weighted inequalities, H1, BMO spaces, and the T1 theorem, are discussed. Chapter 1 presents a review of Fourier series and integrals; Chapters 2 and 3 introduce two operators that are basic to the field: the Hardy-Littlewood maximal function and the Hilbert transform in higher dimensions. Chapters 4 and 5 discuss singular integrals, including modern generalizations. Chapter 6 studies the relationship between H1, BMO, and singular integrals; Chapter 7 presents the elementary theory of weighted norm inequalities. Chapter 8 discusses Littlewood-Paley theory, which had developments that resulted in a number of applications. The final chapter concludes with an important result, the T1 theorem, which has been of crucial importance in the field. This volume has been updated and translated from the original Spanish edition (1995). Minor changes have been made to the core of the book; however, the sections, "Notes and Further Results" have been considerably expanded and incorporate new topics, results, and references. It is geared toward graduate students seeking a concise introduction to the main aspects of the classical theory of singular operators and multipliers. Prerequisites include basic knowledge in Lebesgue integrals and functional analysis.

Harmonic Analysis

María Cristina Pereyra,Lesley A. Ward
Harmonic Analysis Book PDF

Author : María Cristina Pereyra,Lesley A. Ward
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 47,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821875667

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Harmonic Analysis by María Cristina Pereyra,Lesley A. Ward Pdf

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.

Fourier Analysis in Convex Geometry

Alexander Koldobsky
Fourier Analysis in Convex Geometry Book PDF

Author : Alexander Koldobsky
Publisher : American Mathematical Soc.
Page : 170 pages
File Size : 52,6 Mb
Release : 2014-11-12
Category : Electronic
ISBN : 9781470419523

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Fourier Analysis in Convex Geometry by Alexander Koldobsky Pdf

The study of the geometry of convex bodies based on information about sections and projections of these bodies has important applications in many areas of mathematics and science. In this book, a new Fourier analysis approach is discussed. The idea is to express certain geometric properties of bodies in terms of Fourier analysis and to use harmonic analysis methods to solve geometric problems. One of the results discussed in the book is Ball's theorem, establishing the exact upper bound for the -dimensional volume of hyperplane sections of the -dimensional unit cube (it is for each ). Another is the Busemann-Petty problem: if and are two convex origin-symmetric -dimensional bodies and the -dimensional volume of each central hyperplane section of is less than the -dimensional volume of the corresponding section of , is it true that the -dimensional volume of is less than the volume of ? (The answer is positive for and negative for .) The book is suitable for graduate students and researchers interested in geometry, harmonic and functional analysis, and probability. Prerequisites for reading this book include basic real, complex, and functional analysis.