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Fourier Analysis and Integral Transforms
Fourier Analysis and Integral Transforms
foundations +1 more results +53 more equations depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) definition 17.1: Fourier coefficients and Fourier series 17.1 Fourier coeffici… definition 17.25: Multiple Fourier series 17.25 Multiple Fourier… definition 17.29: Fourier transform; the treatise convention 17.29 Fourier transfor… definition 17.38: Schwartz space and tempered distributions 17.38 Schwartz space a… definition 17.40: Transform and derivative of a distribution 17.40 Transform and de… definition 17.50: Convolution 17.50 Convolution definition 17.56: Correlation 17.56 Correlation definition 17.58: Stationary process and power spectral density 17.58 Stationary proce… definition 17.65: One-sided Laplace transform 17.65 One-sided Laplac… definition 17.79: Band-limited function 17.79 Band-limited fun… definition 17.84: Discrete Fourier transform 17.84 Discrete Fourier… definition 17.92: Mellin transform 17.92 Mellin transform definition 17.97: Multiplicative convolution 17.97 Multiplicative c… lemma 17.2: Orthogonality of the harmonics 17.2 Orthogonality of… theorem 17.3: Euler–Fourier coefficient formulas 17.3 Euler–Fourier co… proposition 17.4: Least squares and Bessel's inequality 17.4 Least squares an… lemma 17.6: Dirichlet kernel 17.6 Dirichlet kernel lemma 17.7: Riemann–Lebesgue 17.7 Riemann–Lebesgue corollary 17.8: Localisation 17.8 Localisation theorem 17.9: Dirichlet 17.9 Dirichlet proposition 17.10: Smoothness and coefficient decay 17.10 Smoothness and c… corollary 17.11: Uniform convergence for C^1
functions 17.11 Uniform converge… lemma 17.12: Divergence of the Lebesgue constants 17.12 Divergence of th… theorem 17.13: du Bois-Reymond 17.13 du Bois-Reymond lemma 17.14: Uniformly bounded sine sums 17.14 Uniformly bounde… lemma 17.15: A polynomial whose partial sum spikes at the origin 17.15 A polynomial who… equation 17.11: eq:ft-square-coefficients eq. (17.11) equation 17.38: eq:ft-derivative eq. (17.38) equation 17.37: eq:ft-scaling eq. (17.37) equation 17.35: eq:ft-translation eq. (17.35) equation 17.42: eq:ft-gaussian eq. (17.42) equation 17.92: eq:ft-kramers-kronig eq. (17.92) equation 17.109: eq:ft-mellin-gamma eq. (17.109) The chain of Fourier Analysis and Integral Transforms: 33 of 87 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.