Product Description
This modern introduction to Fourier analysis and partial differential equations is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations, including a fairly complete discussion of local and global well-posedness for the nonlinear Schrödinger and the Korteweg-de Vries equations; they turn their attention, in the two final chapters, to the nonperiodic setting, concentrating on problems that do not occur in the periodic case. ... Read more

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In all areas of modelling and numerical simulation scientists and engineers are faced with problems that require a collection of mathematical tools ranging from the classical - the Fourier transform, convolution, distributions - to the more recent wavelet-based techniques.

For this reason, the object of this text, which focuses on Fourier analysis, signal analysis and filters, is two-fold. On the one hand it conveys to the mathematician a rigorous presentation illustrated with important practical applications of the theory, including a discussion of Fast Fourier Transform. On the other hand it imparts to the physicist and engineer a body of theory in which the `well-known' formulae find their justification.

There is a systematic development of fundamental concepts, such as the Lebesgue integration and theory of distribution, that allows one to establish precise relations among several domains: Fourier transform and convolution; filtering and sampling; time-frequency analysis (gabor transforms and wavelets).

Each of the 42 lectures provides an easily assimilated set of ideas and techniques, suitable for both classroom or self-study. Maneuvering through the book is facilitatedby grouping the lectures into 12 chapters and by adding numerous summary tables. This latter feature makes the book a handy reference for the subjects covered.

Senior undergraduate and graduate students in engineering, physics and mathematics will find this book helpful. It will also serve as a useful reference for scientists and engineers who deal with modelling and signal processing. ... Read more

Customer Reviews (1)

An excellent text for Fourier Analysis
I bought this book hoping to find a self-contained, semi-rigorous introduction to Fourier Analysis and its applications, and indeed I'm very pleased with the purchase. One aspect of the book's format that I enjoyed in a self-study setting is how it is partitioned into lessons (which are in turn divided into chapters). Indeed, it seemed that each lesson took me about 60-90 minutes to absorb, which is the average time most students (including myself) devote to one lesson.

Another aspect of the book I enjoyed was the fact that, on one hand the author took the time to introduce mathematically sophisticated ideas such as Lesbesgue measure and Hilbert spaces in order to make the proofs run more smoothly, but on the other there where more practical lessons on the fast Fourier transform, filters, and even wavelet analysis (last lesson). Such a blend of theory and practice in a relatively compact text seems quite rare.

Finally, I highly recommend this book for students of all levels; but especially to graduate students in mathematics, physics, and engineering. ... Read more

Product Description
A companion volume to Weaver's Applications of Discrete and Continuous Fourier Analysis (Wiley, 1983). Addresses the theoretical and analytical aspects of Fourier analysis, including topics usually found only in more advanced treatises. Provides background information before going on to cover such topics as existence of the inner product, distribution theory, Fourier series representation of complex functions, properties and behavior of the Fourier transform, Fourier transform of a distribution, physical interpretation of convolution, the fast Fourier transform, sampling a function, and much more. Includes exercises, problems, applications, over 150 illustrations, and a Fourier transform FORTRAN subroutine. ... Read more

Customer Reviews (1)

Excellent teaching book, Excellent reference book
Weaver's book is exceptionally well-written, with clear step-by-step explanations of each concept.It is a great teaching tool, and a great reference book.It is one of the few books in which I can quickly find the answer I need. ... Read more

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The second in a two-volume series on signal analysis, this book draws on the foundations laid in the first volume to survey the diverse applications of sampling theory both within mathematics and in other areas of science. Topics include combinatorial analysis, number theory, neural networks, derivative sampling, wavelets, stochastic signals, random fields, and abstract harmonic analysis. ... Read more

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This self-contained anduser-friendly textbook is designed for a first, one-semester course in statistical signal analysis for a broad audience of students inengineering and the physical sciences. The emphasis throughout is on fundamental concepts and relationships in the statistical theory of stationary random signals, which are explained in a concise, yet rigorous presentation. With abundant practice exercises and thorough explanations, A First Course in Statistics for Signal Analysis is an excellent tool for both teaching students and training laboratory scientists and engineers. Improvements in the second edition include considerably expanded sections, enhanced precision, and more illustrative figures.

Customer Reviews (1)

An excellent introduction
This text serves as an excellent introduction to statistics for signal analysis.Be aware that it emphasizes theory over numerical methods - and that it is dense.If one is not looking for lengthy explanations but instead wants to get to the point quickly this book may be for them. ... Read more

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Vol. 1 of Lars Hörmander's influential 4-volume treatise is a detailed exposition of the theory of distributions. From the reviews: 'In order to illustrate the richness of the book: in my review of the 1983 edition [...] I gave a list of 20 subjects which were new compared to Hörmander's book of 1963. Most of these subjects concern important, basic and highly nontrivial theorems in analysis. Hörmander's treatment of these is extremely clear and efficient and often highly original. [...] Most of the exercises are witty, with an interesting point. The phrasing of both the exercises and the answers and hints is very careful [...] In all, the book can be highly recommended, both as a textbook for advanced students, and as background and reference for introductory courses on distributions and Fourier analysis. J.J. Duistermaat in Mededelingen van het Wiskundig Genootschap. ... Read more

Customer Reviews (1)

the definitive guide to micro-local analysis
Hormander's four volume guide to linear partial differential operators is the definitive guide to smooth micro-local analysis from the man who invented a large fraction of it.

Micro-local analysis is an approach tothe analysis of singularities of variable coefficient linear partialdifferential equations based on the use of the Fourier transform and ofsymplectic geometry. Ideas from Hamiltonian physics and quantum theory alsofeature heavily. The fact that the subject is a mixture of analysis andgeometry makes it beautiful and powerful.

The four volume set is hardwork and in some ways is more useful as a reference work than as a learningbook but on the other hand, all the material is there and the books doreward the reader who is willing to spend the time to study themcarefully.

The first volume is the most accessible and the secondpaperback edition carries the added benefit of included exercises withpartial answers which are often highly informative. ... Read more

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Examples and Theorems in Analysis takes a unique and very practical approach to mathematical analysis. It makes the subject more accessible by giving the examples equal status with the theorems. The results are introduced and motivated by reference to examples which illustrate their use, and further examples then show how far the assumptions may be relaxed before the result fails. The contents cover: sequences, functions and continuity, differentiation, constructive integration, improper integrals, series, applications.

A number of applications show what the subject is about; the applications in Fourier theory, distributions and asymptotics show how the results may be put to use. Exercises at the end of each chapter, of varying levels of difficulty, develop new ideas and present open problems. Although written primarily for first- and second-year undergraduates in mathematics, this book is an entertaining and stimulating companion that will also appeal to students of statistics, computer science and engineering. ... Read more

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This volume is a useful introduction to the subject of Fourier Integral Operators and is based on the author’s classic set of notes. Covering a range of topics from Hörmander’s exposition of the theory, Duistermaat approaches the subject from symplectic geometry and includes application to hyperbolic equations (= equations of wave type) and oscillatory asymptotic solutions which may have caustics. This text is suitable for mathematicians and (theoretical) physicists with an interest in (linear) partial differential equations, especially in wave propagation, rep. WKB-methods.

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Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous examples, completely worked out, together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable in using advanced mathematical tools in junior, senior, and beginning graduate courses.

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A reader-friendly, systematic introduction to Fourier analysis

Rich in both theory and application, Fourier Analysis presents a unique and thorough approach to a key topic in advanced calculus. This pioneering resource tells the full story of Fourier analysis, including its history and its impact on the development of modern mathematical analysis, and also discusses essential concepts and today's applications.

Written at a rigorous level, yet in an engaging style that does not dilute the material, Fourier Analysis brings two profound aspects of the discipline to the forefront: the wealth of applications of Fourier analysis in the natural sciences and the enormous impact Fourier analysis has had on the development of mathematics as a whole. Systematic and comprehensive, the book:

• Presents material using a cause-and-effect approach, illustrating where ideas originated and what necessitated them
• Includes material on wavelets, Lebesgue integration, L2 spaces, and related concepts
• Conveys information in a lucid, readable style, inspiring further reading and research on the subject
• Provides exercises at the end of each section, as well as illustrations and worked examples throughout the text

Based upon the principle that theory and practice are fundamentally linked, Fourier Analysis is the ideal text and reference for students in mathematics, engineering, and physics, as well as scientists and technicians in a broad range of disciplines who use Fourier analysis in real-world situations. ... Read more

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A. Figá Talamanca: Random Fourier series on compact groups.- S. Helgason: Representations of semisimple Lie groups.- H. Jacquet: Représentations des groupes linéaires p-adiques.- G.W. Mackey: Infinite-dimensional group representations and their applications. ... Read more

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Over the course of the last century, the systematic exploration of the relationship between Fourier analysis and other branches of mathematics has lead to important advances in geometry, number theory, and analysis, stimulated in part by Hurwitz's proof of the isoperimetric inequality using Fourier series.

This unified, self-contained volume is dedicated to Fourier analysis, convex geometry, and related topics. Specific topics covered include: * the geometric properties of convex bodies * the study of Radon transforms * the geometry of numbers * the study of translational tilings using Fourier analysis * irregularities in distributions * Lattice point problems examined in the context of number theory, probability theory, and Fourier analysis * restriction problems for the Fourier transform

The book presents both a broad overview of Fourier analysis and convexity as well as an intricate look at applications in some specific settings; it will be useful to graduate students and researchers in harmonic analysis, convex geometry, functional analysis, number theory, computer science, and combinatorial analysis. A wide audience will benefit from the careful demonstration of how Fourier analysis is used to distill the essence of many mathematical problems in a natural and elegant way.