Theorems · Theorem · harmonic analysis
MeasureTheory.Integrable.fourier_smul
∀ {T : ℝ} [hT : Fact (0 < T)] {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E]
{f : AddCircle T → E},
MeasureTheory.Integrable f AddCircle.haarAddCircle →
∀ (n : ℤ), MeasureTheory.Integrable (fun t => (fourier n) t • f t) AddCircle.haarAddCircle- Defined in
- Mathlib.Analysis.Fourier.AddCircle
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 218 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- Factstatement and proof · cited by 2,726
- ContinuousMapstatement · cited by 2,491
- le_reflproof · cited by 2,061
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- AddSubgroup.zmultiplesstatement · cited by 493
- AddCirclestatement and proof · cited by 189
Cited by1
Results whose statement or proof uses this declaration.
- fourierCoeff.addproof · cited by 2