| import Mathlib.Analysis.Fourier.AddCircle | |
| namespace OAI | |
| noncomputable section | |
| namespace Invariant233.Fejer | |
| abbrev Circle := AddCircle (1 : ℝ) | |
| def geometricPolynomial (H : ℕ) (x : Circle) : ℂ := | |
| ∑ k ∈ Finset.range H, fourier (k : ℤ) x | |
| def kernel (H : ℕ) (x : Circle) : ℝ := | |
| Complex.normSq (geometricPolynomial H x) / H | |
| def frequencies (H : ℕ) : Finset ℤ := Finset.Ioo (-(H : ℤ)) (H : ℤ) | |
| def coefficient (H : ℕ) (n : ℤ) : ℂ := | |
| fourierCoeff (fun x : Circle => (kernel H x : ℂ)) n | |
| end Invariant233.Fejer | |
| end | |
| end OAI | |