Theorems · Theorem · harmonic analysis
UnitAddTorus.mFourierCoeff_toLp
∀ {d : Type u_1} [inst : Fintype d] (f : C(UnitAddTorus d, ℂ)) (n : d → ℤ),
UnitAddTorus.mFourierCoeff (↑↑((ContinuousMap.toLp 2 MeasureTheory.volume ℂ) f)) n = UnitAddTorus.mFourierCoeff (⇑f) n- Defined in
- Mathlib.Analysis.Fourier.AddCircleMulti
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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 · cited by 25,697
- RingHom.idstatement · cited by 18,349
- ENNRealstatement · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Complexstatement and proof · cited by 5,565
- ContinuousLinearMapstatement · cited by 5,352
- AddSubgroupstatement · cited by 3,232
- ContinuousMapstatement and proof · cited by 2,491
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- MeasureTheory.AEEqFunstatement · cited by 856
- MeasureTheory.Lpstatement · cited by 715
Cited by1
Results whose statement or proof uses this declaration.
- UnitAddTorus.hasSum_mFourier_series_of_summableproof · cited by 1