Theorems · Theorem · harmonic analysis
orthonormal_fourier
∀ {T : ℝ} [hT : Fact (0 < T)], Orthonormal ℂ (fourierLp 2)The monomials fourier n are an orthonormal set with respect to normalised Haar measure.
- Defined in
- Mathlib.Analysis.Fourier.AddCircle
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 267 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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 · cited by 9,879
- Complexstatement and proof · cited by 5,565
- AddSubgroupstatement · cited by 3,232
- Factstatement and proof · cited by 2,726
- MeasureTheory.integralproof · cited by 1,779
- one_smulproof · cited by 1,374
- MeasureTheory.AEEqFunstatement · cited by 856
- zero_smulproof · cited by 716
- MeasureTheory.Lpstatement · cited by 715
- AddSubgroup.zmultiplesstatement · cited by 493
Cited by4
Results whose statement or proof uses this declaration.
- fourierBasisproof · cited by 5
- coe_fourierBasisproof · cited by 3
- fourierCoeff_fourierproof · cited by 1
- UnitAddTorus.orthonormal_mFourierproof · cited by 1