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.
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.
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
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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