Theorems · Definition
FourierTransform.fourier
{E : Type u} → {F : outParam (Type v)} → [self : FourierTransform E F] → E → F𝓕 f is the Fourier transform of f. The meaning of this notation is type-dependent.
- Defined in
- Mathlib.Analysis.Fourier.Notation
- Cited by
- 130 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 3 definitions · uses no axioms
- Assumes
- FourierTransform
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FourierTransformstatement and proof · cited by 23
Cited by149
Results whose statement or proof uses this declaration.
- FourierInvPair.fourier_fourierInv_eqstatement · cited by 10
- FourierPair.fourierInv_fourier_eqstatement · cited by 7
- SchwartzMap.fourierMultiplierCLM_applystatement · cited by 7
- SchwartzMap.convolutionproof · cited by 6
- Real.Lp.fourierTransformproof · cited by 5
- TemperedDistribution.fourierMultiplierCLM_applystatement · cited by 5
- TemperedDistribution.fourierMultiplierCLM_fourierMultiplierCLM_applyproof · cited by 5
- Real.fourierInv_eq_fourier_negstatement · cited by 4
- FourierSMul.fourier_smulstatement · cited by 4
- TemperedDistribution.fourier_toTemperedDistributionCLM_eqstatement and proof · cited by 3
- Complex.tsum_exp_neg_quadraticproof · cited by 3
- Real.fourier_bilin_convolution_eqstatement · cited by 3