Theorems · Definition · harmonic analysis
fourier
{T : ℝ} → ℤ → C(AddCircle T, ℂ)The family of exponential monomials fun x => exp (2 π i n x / T), parametrized by n : ℤ and
considered as bundled continuous maps from ℝ / ℤ • T to ℂ.
- Defined in
- Mathlib.Analysis.Fourier.AddCircle
- Cited by
- 62 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexstatement · cited by 5,565
- ContinuousMapstatement · cited by 2,491
- AddSubgroup.zmultiplesstatement · cited by 493
- AddCirclestatement and proof · cited by 189
- AddCircle.toCircleproof · cited by 41
Cited by66
Results whose statement or proof uses this declaration.
- fourierCoeffproof · cited by 26
- UnitAddTorus.mFourierproof · cited by 15
- fourierLpproof · cited by 9
- fourier_applystatement · cited by 7
- fourier_coe_applystatement · cited by 7
- fourierCoeffOn_eq_integralstatement and proof · cited by 5
- fourier_zerostatement · cited by 5
- Real.hasDerivAt_fourierCharproof · cited by 4
- fourierCoeff_eq_intervalIntegralstatement and proof · cited by 4
- Complex.tsum_exp_neg_quadraticproof · cited by 3
- orthonormal_fourierproof · cited by 3
- Polynomial.fourierCoeff_toAddCircleproof · cited by 3