Theorems · Theorem · harmonic analysis
fourierCoeff.add
∀ {T : ℝ} [hT : Fact (0 < T)] {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E]
{f g : AddCircle T → E},
MeasureTheory.Integrable f AddCircle.haarAddCircle →
MeasureTheory.Integrable g AddCircle.haarAddCircle → fourierCoeff (f + g) = fourierCoeff f + fourierCoeff g- Defined in
- Mathlib.Analysis.Fourier.AddCircle
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Factstatement and proof · cited by 2,726
- MeasureTheory.integralproof · cited by 1,779
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- AddSubgroup.zmultiplesstatement · cited by 493
- smul_addproof · cited by 263
- AddCirclestatement and proof · cited by 189
- fourierproof · cited by 62
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.fourierCoeff_toAddCircleproof · cited by 3
- fourierCoeff.sumproof · cited by 0