theorem 17.36 Plancherel

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theorem 17.36: Plancherel17.36definition 17.29: Fourier transform; the treatise convention17.29theorem 17.32: Fourier inversion17.32theorem 17.43: Bandwidth theorem17.43proof : ch:15-fourier-integral-transforms@proof-24proofcorollary 17.49: Lattice sums and the reciprocal lattice17.49definition 17.79: Band-limited function17.79definition 17.58: Stationary process and power spectral density17.58definition 25.52: Wigner function25.52example 17.31: The three standard pairs17.31lemma A.584: Fourier injectivity in n variablesA.584lemma 17.35: Multiplication formula17.35proposition 17.90: Hankel transform as the axially symmetric Fourier transform17.90proposition 17.68: The Laplace transform is a Fourier transform17.68proposition 17.30: Elementary properties17.30proposition 28.60: A wave packet translates at v_g and spreads at a rate set by the curvature of \omega(k)28.60proposition 10.39: Fourier reduction on the line10.39theorem 17.53: Convolution theorem17.53theorem 17.78: Causality implies dispersion relations17.78theorem 17.47: Poisson summation17.47theorem 17.104: Projection-slice theorem17.104theorem 17.59: Wiener–Khinchin17.59equation 17.42: eq:ft-gaussian17.42corollary 17.81: Sampling periodises the spectrum; aliasing17.81corollary 17.33: The transform is injective17.33proposition 17.41: The identities physics uses17.41proposition 17.42: Sokhotski–Plemelj17.42proposition 17.39: The transform preserves S17.39theorem 17.69: Bromwich inversion integral17.69theorem 17.106: Filtered back-projection in a plane slice17.106theorem 17.94: Mellin inversion17.94theorem 17.105: Radon inversion in three-dimensional space17.105theorem 17.80: Sampling theorem17.80theorem 25.53: Properties of the Wigner function25.53proof : ch:15-fourier-integral-transforms@proof-20proofcorollary 17.44: Duration and bandwidth in SI17.44remark 17.46: The quantum reading, in SI17.46proof : ch:15-fourier-integral-transforms@proof-28proof

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cites Contribution À ĽÉtude de la reprÉsentation D'une fonction arbitraire par des intÉgrales dÉfinies derived parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1446
depends_on Fourier transform; the treatise convention declared parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1447
depends_on Fourier inversion declared parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1447
depends_on Bandwidth theorem declared parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1718
proves ch:15-fourier-integral-transforms@proof-24 declared parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1450