M. R. Gabdullin

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20202023

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math.CA2023

Trigonometric polynomials with frequencies in the set of cubes

Mikhail R. Gabdullin, Sergei V. Konyagin

We prove that for any $ε > 0$ and any trigonometric polynomial $f$ with frequencies in the set ${n^{3} : N \leq n \leq N + N^{2/3 - ε}}$ , one has $∥ f ∥_{4} ≪ ε^{- 1/4} ∥ f ∥_{2}$ with imp…

math.CA2021

Trigonometric series with noninteger harmonics

Mikhail R. Gabdullin

Let ${c_{k}}$ be a nonincreasing sequence of positive numbers (more general classes of sequences are also considered), and $α > 0$ be not an integer. We find necessary and sufficient…