Theorems · Theorem · harmonic analysis
UnitAddTorus.coe_mFourierBasis
∀ {d : Type u_1} [inst : Fintype d], ⇑UnitAddTorus.mFourierBasis = UnitAddTorus.mFourierLp 2The elements of the Hilbert basis mFourierBasis are the functions mFourierLp 2, i.e. the
monomials mFourier n on UnitAddTorus d considered as elements of L².
- Defined in
- Mathlib.Analysis.Fourier.AddCircleMulti
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 272 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- ENNRealstatement · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Complexstatement · cited by 5,565
- AddSubgroupstatement · cited by 3,232
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- MeasureTheory.AEEqFunstatement · cited by 856
- MeasureTheory.Lpstatement · cited by 715
- UnitAddCirclestatement · cited by 157
- UnitAddTorusstatement · cited by 29
- HilbertBasisstatement · cited by 28
- UnitAddTorus.mFourierLpstatement · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- UnitAddTorus.mFourierBasis_reprproof · cited by 1