KnowraFourier inversion theoremLinked fromLinked fromThe 7 pages that link to Fourier inversion theorem, each with the reason it gives.All 7Related 7Fourier transformRelated: It explains when the frequency representation preserves enough information for exact reconstruction.Harmonic analysisRelated: It establishes when the frequency representation determines the original function.Poisson summation formulaRelated: The formula’s normalization and scaling depend on the Fourier transform convention used for inversion.Jordan's lemmaRelated: Contour evaluation of oscillatory integrals can establish inversion formulas in particular cases.Riemann–Lebesgue lemmaRelated: Decay of the transform supports inversion arguments but is weaker than an inversion result.Pontryagin dualityRelated: Duality explains why inversion exchanges a group and its character group.Berry–Esseen theoremRelated: It supports the analytic step that turns transform estimates into a bound on distribution functions.