Theorems · Definition · harmonic analysis
fourierLp
{T : ℝ} → [hT : Fact (0 < T)] → (p : ENNReal) → [Fact (1 ≤ p)] → ℤ → ↥(MeasureTheory.Lp ℂ p AddCircle.haarAddCircle)The family of monomials fourier n, parametrized by n : ℤ and considered as
elements of the Lp space of functions AddCircle T → ℂ.
- Defined in
- Mathlib.Analysis.Fourier.AddCircle
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- ENNRealstatement and proof · cited by 9,879
- Complexstatement and proof · cited by 5,565
- AddSubgroupstatement · cited by 3,232
- Factstatement and proof · cited by 2,726
- MeasureTheory.AEEqFunstatement · cited by 856
- MeasureTheory.Lpstatement · cited by 715
- AddSubgroup.zmultiplesstatement · cited by 493
- AddCirclestatement · cited by 189
- fourierproof · cited by 62
- AddCircle.haarAddCirclestatement and proof · cited by 28
Cited by9
Results whose statement or proof uses this declaration.
- orthonormal_fourierstatement · cited by 3
- coe_fourierBasisstatement · cited by 3
- coeFn_fourierLpstatement · cited by 2
- hasSum_fourier_series_L2statement and proof · cited by 1
- hasSum_fourier_series_of_summableproof · cited by 1
- fourierBasis_reprproof · cited by 1
- fourierCoeff_fourierproof · cited by 1
- span_fourierLp_closure_eq_topstatement and proof · cited by 0
- fourierLp.congr_simpstatement and proof · cited by 0