Theorems · Theorem · harmonic analysis
hasDerivAt_fourier
∀ (T : ℝ) (n : ℤ) (x : ℝ), HasDerivAt (fun y => (fourier n) ↑y) (2 * ↑Real.pi * Complex.I * ↑n / ↑T * (fourier n) ↑x) x
- Defined in
- Mathlib.Analysis.Fourier.AddCircle
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- TopologicalSpaceproof · cited by 24,529
- Moduleproof · cited by 20,661
- AddCommGroupproof · cited by 12,871
- NontriviallyNormedFieldproof · cited by 8,742
- Complexstatement and proof · cited by 5,565
- ContinuousMapstatement · cited by 2,491
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- ContinuousSMulproof · cited by 1,016
- Complex.Istatement and proof · cited by 866
Cited by2
Results whose statement or proof uses this declaration.
- Real.hasDerivAt_fourierCharproof · cited by 4
- hasDerivAt_fourier_negproof · cited by 1