Theorems · Theorem · harmonic analysis
Real.fourier_iteratedDeriv
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : ℝ → E} {N : ℕ∞} {n : ℕ},
ContDiff ℝ (↑N) f →
(∀ (n : ℕ), ↑n ≤ N → MeasureTheory.Integrable (iteratedDeriv n f) MeasureTheory.volume) →
↑n ≤ N →
FourierTransform.fourier (iteratedDeriv n f) = fun x =>
(2 * ↑Real.pi * Complex.I * ↑x) ^ n • FourierTransform.fourier f x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 292 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- ENatstatement and proof · cited by 4,985
- InnerProductSpaceproof · cited by 3,523
- Finset.univproof · cited by 3,473
- one_mulproof · cited by 2,841
- SeminormedAddCommGroupproof · cited by 2,671
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.