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Theorems · Theorem

FourierPair.fourierInv_fourier_eq

∀ {E : Type u_5} {F : Type u_6} {inst : FourierTransform E F} {inst_1 : FourierTransformInv F E}
  [self : FourierPair E F] (f : E), FourierTransformInv.fourierInv (FourierTransform.fourier f) = f
Defined in
Mathlib.Analysis.Fourier.Notation
Cited by
7 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
FourierPair
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FourierTransform.fourierEquiv · cited by 4FourierTransform.fourierE…TemperedDistribution.lineDeriv_eq_fourierMultiplierCLM · cited by 2TemperedDistribution.line…SchwartzMap.lineDeriv_eq_fourierMultiplierCLM · cited by 1SchwartzMap.lineDeriv_eq_…SchwartzMap.integral_sesq_fourier_fourier · cited by 1SchwartzMap.integral_sesq…TemperedDistribution.fourierInv_toTemperedDistributionCLM_eq · cited by 1TemperedDistribution.four…MeasureTheory.Lp.fourierInv_toTemperedDistribution_eq · cited by 1Lp.fourierInv_toTemperedD…SchwartzMap.fourierMultiplierCLM_const · cited by 0SchwartzMap.fourierMultip…SchwartzMap.convolution_apply · cited by 0SchwartzMap.convolution_a…FourierTransform.fourier · cited by 130FourierTransform.fourierFourierTransformInv.fourierInv · cited by 69FourierTransformInv.fouri…FourierTransformInv · cited by 25FourierTransformInvFourierTransform · cited by 23FourierTransformFourierPair · cited by 7FourierPairFourierPair.fourierInv_fourie…CITED BYCITES

Cites5

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Cited by8

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