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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

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