Point evaluation for polynomials on the circle

2025/09/26 by Instanes, Sarah May
#26D05 (secondary) #42A05 (primary) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.22035

Abstract

We study the constant \mathscrC_d,p defined as the smallest constant C such that ‖P‖_∞^p ≤ C‖P‖_p^p holds for every polynomial P of degree d, where we consider the L^p norm on the unit circle. We conjecture that \mathscrC_d,p ≤ dp/2+1 for all p ≥ 2 and all degrees d. We show that the conjecture holds for all p ≥ 2 when d ≤ 4 and for all d when p ≥ 6.8.

Citations

• An optimization problem and point-evaluation in Paley-Wiener spaces

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