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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2311.14937 |
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| _version_ | 1866917609058861056 |
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| author | Gabdullin, Mikhail R. Konyagin, Sergei V. |
| author_facet | Gabdullin, Mikhail R. Konyagin, Sergei V. |
| contents | 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 $$ \|f\|_4 \ll ε^{-1/4}\|f\|_2 $$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14937 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Trigonometric polynomials with frequencies in the set of cubes Gabdullin, Mikhail R. Konyagin, Sergei V. Classical Analysis and ODEs 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 $$ \|f\|_4 \ll ε^{-1/4}\|f\|_2 $$ 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. |
| title | Trigonometric polynomials with frequencies in the set of cubes |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2311.14937 |