Theorems · Theorem · harmonic analysis
fourier_apply
∀ {T : ℝ} {n : ℤ} {x : AddCircle T}, (fourier n) x = ↑(n • x).toCircle- Defined in
- Mathlib.Analysis.Fourier.AddCircle
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- Complexstatement · cited by 5,565
- Submonoidstatement · cited by 3,086
- ContinuousMapstatement · cited by 2,491
- AddSubgroup.zmultiplesstatement · cited by 493
- AddCirclestatement and proof · cited by 189
- Submonoid.unitSpherestatement · cited by 85
- fourierstatement · cited by 62
- AddCircle.toCirclestatement · cited by 41
Cited by7
Results whose statement or proof uses this declaration.
- fourier_coe_applyproof · cited by 7
- fourier_neg'proof · cited by 3
- fourier_oneproof · cited by 2
- fourier_coe_apply'proof · cited by 2
- MeasureTheory.Integrable.fourier_smulproof · cited by 1
- fourier_add'proof · cited by 1
- fourier_add_half_inv_indexproof · cited by 1