Theorems · Theorem · harmonic analysis
UnitAddTorus.mFourierBasis_repr
∀ {d : Type u_1} [inst : Fintype d] (f : ↥(MeasureTheory.Lp ℂ 2 MeasureTheory.volume)) (i : d → ℤ),
↑(UnitAddTorus.mFourierBasis.repr f) i = UnitAddTorus.mFourierCoeff (↑↑f) iUnder the isometric isomorphism mFourierBasis from L²(UnitAddTorus d) to ℓ²(ℤᵈ, ℂ),
the i-th coefficient is mFourierCoeff f i.
- Defined in
- Mathlib.Analysis.Fourier.AddCircleMulti
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 273 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.
Cites33
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- 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
- AddSubgroupstatement · cited by 3,232
- mul_commproof · cited by 2,262
- MeasureTheory.integralproof · cited by 1,779
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Inner.innerproof · cited by 1,089
Cited by1
Results whose statement or proof uses this declaration.
- UnitAddTorus.hasSum_mFourier_series_L2proof · cited by 1