Theorems · Definition · harmonic analysis
UnitAddTorus.mFourierLp
{d : Type u_1} →
[inst : Fintype d] → (p : ENNReal) → [Fact (1 ≤ p)] → (d → ℤ) → ↥(MeasureTheory.Lp ℂ p MeasureTheory.volume)The family of monomials mFourier n, parametrized by n : ℤᵈ and considered as
elements of the Lp space of functions UnitAddTorus d → ℂ.
- Defined in
- Mathlib.Analysis.Fourier.AddCircleMulti
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 235 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
- ENNRealstatement and proof · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Complexstatement and proof · cited by 5,565
- AddSubgroupstatement · cited by 3,232
- Factstatement and proof · cited by 2,726
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- MeasureTheory.AEEqFunstatement · cited by 856
- MeasureTheory.Lpstatement · cited by 715
- UnitAddCirclestatement · cited by 157
- UnitAddTorusstatement · cited by 29
- ContinuousMap.toLpproof · cited by 21
Cited by8
Results whose statement or proof uses this declaration.
- UnitAddTorus.hasSum_mFourier_series_L2statement · cited by 1
- UnitAddTorus.hasSum_mFourier_series_of_summableproof · cited by 1
- UnitAddTorus.mFourierBasis_reprproof · cited by 1
- UnitAddTorus.orthonormal_mFourierstatement · cited by 1
- UnitAddTorus.coeFn_mFourierLpstatement · cited by 1
- UnitAddTorus.coe_mFourierBasisstatement · cited by 1
- UnitAddTorus.span_mFourierLp_closure_eq_topstatement · cited by 0
- UnitAddTorus.mFourierLp.congr_simpstatement and proof · cited by 0