proof ch:15-fourier-integral-transforms@proof-20

open in the book · parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1312

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proof : ch:15-fourier-integral-transforms@proof-20prooftheorem 17.32: Fourier inversion17.32definition 17.29: Fourier transform; the treatise convention17.29equation 17.42: eq:ft-gaussian17.42corollary 17.81: Sampling periodises the spectrum; aliasing17.81corollary 17.33: The transform is injective17.33lemma A.584: Fourier injectivity in n variablesA.584proposition 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 17.53: Convolution theorem17.53theorem 17.106: Filtered back-projection in a plane slice17.106theorem 17.94: Mellin inversion17.94theorem 17.36: Plancherel17.36theorem 17.105: Radon inversion in three-dimensional space17.105theorem 17.80: Sampling theorem17.80theorem 17.59: Wiener–Khinchin17.59theorem 25.53: Properties of the Wigner function25.53

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typedirectionnode provenancewhere
cites Théorie analytique de la chaleur derived parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1314
cites Introduction to the Theory of Fourier Integrals derived parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1316
proves Fourier inversion declared parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1312