Theorems · Theorem · harmonic analysis
tsum_sq_fourierCoeff
- 1000+ list: Parseval's theorem
∀ {T : ℝ} [hT : Fact (0 < T)] (f : ↥(MeasureTheory.Lp ℂ 2 AddCircle.haarAddCircle)),
∑' (i : ℤ), ‖fourierCoeff (↑↑f) i‖ ^ 2 = ∫ (t : AddCircle T), ‖↑↑f t‖ ^ 2 ∂AddCircle.haarAddCircle- Defined in
- Mathlib.Analysis.Fourier.AddCircle
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 273 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.
Cites18
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
- ENNRealstatement · cited by 9,879
- Complexstatement and proof · cited by 5,565
- Norm.normstatement · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- Factstatement and proof · cited by 2,726
- SummationFilter.unconditionalstatement · cited by 2,068
- MeasureTheory.integralstatement · cited by 1,779
- tsumstatement · cited by 1,148
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- MeasureTheory.Lpstatement and proof · cited by 715
- AddSubgroup.zmultiplesstatement · cited by 493
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.sum_sq_norm_coeff_eq_circleAverageproof · cited by 1