Harmonic Analysis and Applications / Edition 1

Harmonic Analysis and Applications / Edition 1

5.0 1
by John J. Benedetto
     
 

ISBN-10: 0849378796

ISBN-13: 9780849378799

Pub. Date: 07/29/1996

Publisher: Taylor & Francis

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

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Overview

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.

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Product Details

ISBN-13:
9780849378799
Publisher:
Taylor & Francis
Publication date:
07/29/1996
Series:
Studies in Advanced Mathematics Series, #23
Edition description:
New Edition
Pages:
368
Product dimensions:
6.40(w) x 9.55(h) x 0.98(d)

Table of Contents

Prologue I-Course I
Prologue II-Fourier Transforms, Fourier Series, and Discrete Fourier Transforms
Fourier Transforms
Definitions and Formal Calculations
Algebraic Properties of Fourier Transforms
Examples
Analytic Properties of Fourier Transforms
Convolution
Approximate Identities and Examples
Pointwise Inversion of the Fourier Transform
Partial Differential Equations
Gibbs Phenomenon
The L2(R) Theory Exercises
Measures and Distribution Theory
Approximate Identities Definition of Distributions
Differentiation of Distributions
The Fourier Transform of Distributions
Convolution of Distributions
Operational Calculus
Measure Theory
Definitions from Probability Theory
Wiener's Generalized Harmonic Analysis (GHA)
exp{it2}
Exercises
Fourier Series
Fourier Series - Definitions and Convergence
History of Fourier Series
Integration and Differentiation of Fourier Series
The L1(T) and L2(T) Theories A(T) and the Wiener Inversion Theorem Maximum Entropy and Spectral Estimation
Prediction and Spectral Estimation
Discrete Fourier Transform
Fast Fourier Transform
Periodization and Sampling
Exercises
Appendices
A. Real Analysis
B. Functional Analysis
C. Fourier Analysis Formulas
D. Contributors to Fourier Analysis
Notation
Bibliography
Index

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Harmonic Analysis and Applications 5 out of 5 based on 0 ratings. 1 reviews.
Guest More than 1 year ago
I used this book in my teaching of a beginning grad level math (harmonic) analysis course, but relying on three books in all. Harmonic analysis is a big subject with many points of view (infinite in all directions, if you will!). One of the directions is the link to engineering problems. Specific areas of math often serve as service courses for engineers; and harmonic analysis is one area with a rich set of links to engineering problems. Things are complicated however by the the difference in terminology which is used in the two worlds. You might almost say that they speak different languages;-and they have different aims, by necessity! --Benedetto's book makes a heroic, and, in my view, very sucessful effort in highlighting the engineering significance of the basic principles of harmonic analysis. Few harmonic analysis books even try. Benedetto's book may be a bit hard for beginning students(there is a lot in it!), but the investment my students put into it was well worth the effort.