Harmonic Analysis and Applications

ISBN-13: 9780849378799 / Angielski / Twarda / 1996 / 368 str.

John J. Benedetto;Bendetto

Opis

Presents the analysis and synthesis of functions in terms of harmonics in a way that demonstrates the vitality, power, elegance, usefulness of the subject. This work covers the Fourier analysis of integrable and square integrable functions on R, distribution theory, and Fourier series, as well as functions defined on finite intervals.

Recenzje

"Written by a leading specialist in harmonic analysis, the present book is a very good text on harmonic analysis, its applications and evolution, and can be used as a textbook as well as an essay for students and as a general reference for engineers, mathematicians, physicists.."
- Studia University "Babes-Bolyai" Mathematica; Vol XLVI, No. 3, September 2001

Spis treści

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
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

O autorze

Benedetto, John J.