Principles of Fourier Analysis Second Edition

Author: Kenneth B. Howell
Publisher: CRC Press
ISBN: 9781498734080
Release Date: 2016-12-12
Genre: Mathematics

Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas. Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author's development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based on the use of Gaussian test functions that yields an even more general -yet simpler -theory than usually presented. Principles of Fourier Analysis stimulates the appreciation and understanding of the fundamental concepts and serves both beginning students who have seen little or no Fourier analysis as well as the more advanced students who need a deeper understanding. Insightful, non-rigorous derivations motivate much of the material, and thought-provoking examples illustrate what can go wrong when formulas are misused. With clear, engaging exposition, readers develop the ability to intelligently handle the more sophisticated mathematics that Fourier analysis ultimately requires.

A First Course in Harmonic Analysis

Author: Anton Deitmar
Publisher: Springer Science & Business Media
ISBN: 0387228373
Release Date: 2005-03-09
Genre: Mathematics

Affordable softcover second edition of bestselling title (over 1000 copies sold of previous edition) A primer in harmonic analysis on the undergraduate level Gives a lean and streamlined introduction to the central concepts of this beautiful and utile theory. Entirely based on the Riemann integral and metric spaces instead of the more demanding Lebesgue integral and abstract topology. Almost all proofs are given in full and all central concepts are presented clearly. Provides an introduction to Fourier analysis, leading up to the Poisson Summation Formula. Make 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. Introduces 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.

Fourier Analysis in Several Complex Variables

Author: Leon Ehrenpreis
Publisher: Courier Corporation
ISBN: 9780486153032
Release Date: 2011-11-30
Genre: Mathematics

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.

Mathematical Principles of Signal Processing

Author: Pierre Bremaud
Publisher: Springer Science & Business Media
ISBN: 9781475736694
Release Date: 2013-03-14
Genre: Mathematics

From the reviews: "[...] the interested reader will find in Bremaud’s book an invaluable reference because of its coverage, scope and style, as well as of the unified treatment it offers of (signal processing oriented) Fourier and wavelet basics." Mathematical Reviews

Applied Linear Algebra

Author: Lorenzo Adlai Sadun
Publisher: American Mathematical Soc.
ISBN: 9780821844410
Release Date: 2007-12-20
Genre: Mathematics

Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle. Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schrodinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings. Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to Fourier series and the Fourier transform. The second edition contains a series of Explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises.

A Radical Approach to Real Analysis

Author: David M. Bressoud
Publisher: MAA
ISBN: 0883857472
Release Date: 2007-04-12
Genre: Mathematics

Second edition of this introduction to real analysis, rooted in the historical issues that shaped its development.

Reelle und Komplexe Analysis

Author: Walter Rudin
Publisher: Walter de Gruyter
ISBN: 348659186X
Release Date: 2009
Genre: Analysis - Lehrbuch

Besonderen Wert legt Rudin darauf, dem Leser die Zusammenhänge unterschiedlicher Bereiche der Analysis zu vermitteln und so die Grundlage für ein umfassenderes Verständnis zu schaffen. Das Werk zeichnet sich durch seine wissenschaftliche Prägnanz und Genauigkeit aus und hat damit die Entwicklung der modernen Analysis in nachhaltiger Art und Weise beeinflusst. Der "Baby-Rudin" gehört weltweit zu den beliebtesten Lehrbüchern der Analysis und ist in 13 Sprachen übersetzt. 1993 wurde es mit dem renommierten Steele Prize for Mathematical Exposition der American Mathematical Society ausgezeichnet. Übersetzt von Uwe Krieg.

Fourier series transforms and boundary value problems

Author: J. Ray Hanna
Publisher: Wiley-Interscience
ISBN: UOM:39015040048111
Release Date: 1990-07-10
Genre: Mathematics

Retains both the spirit and philosophy of the popular First Edition. The primary changes consist of the addition of new material on integral transforms, discrete and fast Fourier transforms, series solutions, harmonic analysis, spherical harmonics and a glance at some of the numerical techniques for the solution of boundary value problems. With more than enough material for a one-semester course, it offers a full presentation of basic principles, and advanced topics are covered in the largely self-contained closing chapters. The order of presentation of some of the material has been rearranged to provide more flexibility in arranging courses.

A Guided Tour of Mathematical Methods

Author: Roel Snieder
Publisher: Cambridge University Press
ISBN: 0521834929
Release Date: 2004-09-23
Genre: Mathematics

Provides a comprehensive tour of the mathematical methods needed by physical science students.

Fourier Analysis on Finite Groups and Applications

Author: Audrey Terras
Publisher: Cambridge University Press
ISBN: 0521457181
Release Date: 1999-03-28
Genre: Mathematics

A friendly introduction to Fourier analysis on finite groups, accessible to undergraduates/graduates in mathematics, engineering and the physical sciences.

Trigonometric Series

Author: A. Zygmund
Publisher: Cambridge University Press
ISBN: 0521890535
Release Date: 2002
Genre: Mathematics

Both volumes of classic text on trigonometric series, with a foreword by Robert Fefferman.

Advanced Real Analysis

Author: Anthony W. Knapp
Publisher: Springer Science & Business Media
ISBN: 0817644423
Release Date: 2008-07-11
Genre: Mathematics

* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician

Classical and Multilinear Harmonic Analysis

Author: Camil Muscalu
Publisher: Cambridge University Press
ISBN: 9780521882453
Release Date: 2013-01-31
Genre: Mathematics

"This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained, and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderâon-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary, and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderâon's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form"--


Author: John J. Benedetto
Publisher: CRC Press
ISBN: 0849382718
Release Date: 1993-09-27
Genre: Mathematics

Wavelets is a carefully organized and edited collection of extended survey papers addressing key topics in the mathematical foundations and applications of wavelet theory. The first part of the book is devoted to the fundamentals of wavelet analysis. The construction of wavelet bases and the fast computation of the wavelet transform in both continuous and discrete settings is covered. The theory of frames, dilation equations, and local Fourier bases are also presented. The second part of the book discusses applications in signal analysis, while the third part covers operator analysis and partial differential equations. Each chapter in these sections provides an up-to-date introduction to such topics as sampling theory, probability and statistics, compression, numerical analysis, turbulence, operator theory, and harmonic analysis. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. It will be an especially useful reference for harmonic analysts, partial differential equation researchers, signal processing engineers, numerical analysts, fluids researchers, and applied mathematicians.

Advanced Engineering Mathematics

Author: Taneja
Publisher: I. K. International Pvt Ltd
ISBN: 9788189866563
Release Date: 2007-01-01

The text has been divided in two volumes: Volume I (Ch. 1-13) & Volume II (Ch. 14-22). In addition to the review material and some basic topics as discussed in the opening chapter, the main text in Volume I covers topics on infinite series, differential and integral calculus, matrices, vector calculus, ordinary differential equations, special functions and Laplace transforms. Volume II covers topics on complex analysis, Fourier analysis, partial differential equations and statistics. The present book has numerous distinguishing features over the already existing books on the same topic. The chapters have been planned to create interest among the readers to study and apply the mathematical tools. The subject has been presented in a very lucid and precise manner with a wide variety of examples and exercises, which would eventually help the reader for hassle free study.