Theorems · Theorem · harmonic analysis
Real.fourierCoeff_tsum_comp_add
∀ {f : C(ℝ, ℂ)},
(∀ (K : TopologicalSpace.Compacts ℝ),
Summable fun n => ‖ContinuousMap.restrict (↑K) (f.comp (ContinuousMap.addRight ↑n))‖) →
∀ (m : ℤ), fourierCoeff ⋯.lift m = FourierTransform.fourier ⇑f ↑mThe key lemma for Poisson summation: the m-th Fourier coefficient of the periodic function
∑' n : ℤ, f (x + n) is the value at m of the Fourier transform of f.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 263 from the axioms · uses propext, Classical.choice, Quot.sound
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- Real.tsum_eq_tsum_fourierproof · cited by 1