Trigonometric polynomials with frequencies in the set of cubes

Autor:	Gabdullin, Mikhail R., Konyagin, Sergei V.
Rok vydání:	2023
Předmět:	Mathematics - Classical Analysis and ODEs
Druh dokumentu:	Working Paper
Popis:	We prove that for any $\epsilon>0$ and any trigonometric polynomial $f$ with frequencies in the set $\{n^3: N \leq n\leq N+N^{2/3-\epsilon}\}$, one has $$ \|f\|_4 \ll \epsilon^{-1/4}\|f\|_2 $$ 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. Comment: 6 pages; inaccuracy in the proof of the main theorem is corrected
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2311.14937 Zobrazit plný text záznamu View this record from Arxiv