Trigonometric polynomials with frequencies in the set of cubes

2023/11/25 by Mikhail R. Gabdullin, Gabdullin, Mikhail R., Sergeĭ Konyagin +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2311.14937

openalex publication_date 2023/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for any ε>0 and any trigonometric polynomial f with frequencies in the set \n³: N ≤ n≤ N+N^2/3-ε\, one has ‖f‖₄ ≪ ε^-1/4‖f‖₂ with implied constant being absolute. We also show that the set \n³: N≤ n≤ N+(0.5N)^1/2\ is a Sidon set.

Related

• Trigonometric polynomials with frequencies in the set of squares
• The Sidon constant of sets with three elements
• Lower bounds on the measure of the support of positive and negative parts of trigonometric polynomials
• On infinite multiplicative Sidon sets
• On van der Corput property of squares