Bourgain-Ruzsa Type Estimates for the Maximum and Minimum of Littlewood Cosine polynomials on the Real Line

2026/07/24 by Tamás Erdélyi
#math.CA

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Abstract

We prove that max_t ∈ \Bbb RT_n(t) ≥ (1)/(60)n^1/3 \text and -min_t ∈ \Bbb RT_n(t) ≥ (1)/(60)n^1/3 for every trigonometric polynomial T_n of the form T_n(t) = ∑_j=1ⁿcos(jt-θ_j) , θ_j ∈ \Bbb R , t ∈ \Bbb R .

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