Theorems · Theorem · harmonic analysis
Polynomial.sum_sq_norm_coeff_eq_circleAverage
∀ (p : Polynomial ℂ), ∑ i ∈ p.support, ‖p.coeff i‖ ^ 2 = Real.circleAverage (fun θ => ‖Polynomial.eval θ p‖ ^ 2) 0 1
Parseval's Identity for polynomials
- Defined in
- Mathlib.Analysis.Polynomial.Fourier
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 274 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites55
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
- Polynomialstatement and proof · cited by 5,681
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Finset.sumstatement · cited by 5,195
- one_mulproof · cited by 2,841
- zero_addproof · cited by 2,366
- Finset.sum_congrproof · cited by 2,323
- SummationFilter.unconditionalproof · cited by 2,068
- MeasureTheory.integralproof · cited by 1,779
- Real.piproof · cited by 1,774
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.mahlerMeasure_le_sqrt_sum_sq_norm_coeffproof · cited by 1