Theorems · Theorem · harmonic analysis
Real.fourierInv_eq
∀ {V : Type u_1} {E : Type u_3} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [inst_2 : NormedAddCommGroup V]
[inst_3 : InnerProductSpace ℝ V] [inst_4 : MeasurableSpace V] [inst_5 : BorelSpace V] [inst_6 : FiniteDimensional ℝ V]
(f : V → E) (w : V), FourierTransformInv.fourierInv f w = ∫ (v : V), Real.fourierChar (inner ℝ v w) • f v- Cited by
- 3 results in Mathlib
- Foundations
- Depth 252 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- InnerProductSpacestatement and proof · cited by 3,523
- FiniteDimensionalstatement and proof · cited by 1,854
- MeasureTheory.integralstatement and proof · cited by 1,779
- BorelSpacestatement and proof · cited by 1,602
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Inner.innerstatement and proof · cited by 1,089
Cited by3
Results whose statement or proof uses this declaration.
- Real.fourierInv_eq_fourier_negproof · cited by 4
- Real.tendsto_integral_gaussian_smulproof · cited by 1
- Real.fourierInv_eq'proof · cited by 1