Trigonometric Polynomials with Frequencies in the Set of Cubes

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-05 DOI:10.1134/s0001434624030052

M. R. Gabdullin, S. V. Konyagin

引用次数: 0

Abstract

We prove that for any $\varepsilon>0$ and any trigonometric polynomial $f$ with frequencies in the set $\{n^3: N \leq n\leq N+N^{2/3-\varepsilon}\}$ one has

$$\|f\|_4 \ll \varepsilon^{-1/4}\|f\|_2$$

with implied constant being absolute. We also show that the set $\{n^3: N\leq n\leq N+(0.5N)^{1/2}\}$ is a Sidon set.

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具有立方集合中频率的三角多项式

Abstract 我们证明，对于集合 $\{n^3: N \leq n\leq N+N^{2/3-\varepsilon}\}) 中的任意 \(\varepsilon>0$和任意三角多项式 $f$的频率，有 $$\|f\|_4\ll\\varepsilon^{-1/4}\|f\|_2$$，其中隐含的常数是绝对值。我们还证明了集合 \(\{n^3: N\leq n\leq N+(0.5N)^{1/2}\}) 是一个西顿集合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.