TY  - BOOK
AU  - Howell,Kenneth B.
TI  - Principles of Fourier analysis
T2  - Studies in advanced mathematics
SN  - 1420036904 (electronic bk.)
AV  - QA403.5 .H69 2001
U1  - 515/.2433 21
PY  - 2001///
CY  - Boca Raton, Fla.
PB  - Chapman & Hall/CRC
KW  - Fourier analysis
KW  - Fourier, Analyse de
KW  - MATHEMATICS
KW  - Infinity
KW  - bisacsh
KW  - fast
KW  - Electronic books
N1  - Includes bibliographical references (p. 757) and index; 1; The starting point --; 2. Basic terminology, notation, and conventions --; 3; Basic analysis I : continuity and smoothness --; 4; Basic analysis II : integration and infinite series --; 5; Symmetry and periodicity --; 6; Elementary complex analysis --; 7; Functions of several variables --; 8; Heuristic derivation of the Fourier series formulas --; 9; The trigonometric Fourier series --; 10; Fourier series over finite intervals (sine and cosine series) --; 11; Inner products, norms, and orthogonality --; 12; The complex exponential Fourier series --; 13; Convergence and Fourier's conjecture --; 14; Convergence and Fourier's conjecture : the proofs --; 15; Derivatives and integrals of Fourier series --; 16; Applications --; 17; Heuristic derivation of the classical Fourier transform --; 18; Integrals on infinite intervals --; 19; The Fourier integral transforms --; 20; Classical Fourier transforms and classically transformable functions --; 21; Some elementary identities : translation, scaling, and conjugation --; 22; Differentiation and Fourier transforms --; 23; Gaussians and other very rapidly decreasing functions --; 24; Convolution and transforms of products --; 25; Correlation, square-integrable functions, and the fundamental identity of Fourier analysis --; 26; Identity sequences --; 27; Generalizing the classical theory : a naive approach --; 28; Fourier analysis in the analysis of systems --; 29; Gaussians as test functions, and proofs of some important theorems --; 30; A starting point for the generalized theory --; 31; Gaussian test functions --; 32; Generalized functions --; 33; Sequences and series of generalized functions --; 34; Basic transforms of generalized Fourier analysis --; 35; Generalized products, convolutions, and definite integrals --; 36; Periodic functions and regular arrays --; 37; General solutions to simple equations and the pole function --; 38; Periodic, regular arrays --; 39; Sampling and the discrete Fourier transform
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