John J. Benedetto

Harmonic Analysis and Applications (eBook, ePUB)

• Format: ePub

Produktbeschreibung

Harmonic analysis plays an essential role in understanding a host of engineering, mathematical, and scientific ideas. Harmonic Analysis and Applications presents the analysis and synthesis of functions in terms of harmonics in a way that clearly demonstrates the vitality, power, elegance, usefulness of the subject.

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Produktdetails

• Verlag: Taylor & Francis eBooks
• Seitenzahl: 368
• Erscheinungstermin: 17. Dezember 2020
• Englisch
• ISBN-13: 9781000142211
• Artikelnr.: 60688526

Autorenporträt

Benedetto, John J.

Inhaltsangabe

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