Rubrique secondaire: Analyse Harmonique / Harmonic Analysis Titre français: Preuve de la conjecture de quasi-orthogonalité de Saffari pour les suites ultra-plates de polynômes unimodulaires. PROOF OF SAFFARI’S NEAR-ORTHOGONALITY CONJECTURE FOR ULTRAFLAT SEQUENCES OF UNIMODULAR POLYNOMIALS

Abstract

Let Pn(z) = ∑n k=0 ak,nz k ∈ C [z] be a sequence of unimodular polynomials (|ak,n| = 1 for all k, n) which is ultraflat in the sense of Kahane, i.e., lim n→∞ max |z|=1 ∣∣∣(n + 1)−1/2|Pn(z)| − 1∣∣∣ = 0 . We prove the following conjecture of Saffari (1991): ∑n k=0 ak,nan−k,n = o(n) as n → ∞, that is, the polynomial Pn(z) and its “conjugate reciprocal” P ∗ n(z… (More)

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@inproceedings{Erdlyi2013RubriqueSA, title={Rubrique secondaire: Analyse Harmonique / Harmonic Analysis Titre français: Preuve de la conjecture de quasi-orthogonalité de Saffari pour les suites ultra-plates de polynômes unimodulaires. PROOF OF SAFFARI’S NEAR-ORTHOGONALITY CONJECTURE FOR ULTRAFLAT SEQUENCES OF UNIMODULAR POLYNOMIALS}, author={Tam{\'a}s Erd{\'e}lyi}, year={2013} }