On sets of orthogonal exponentials on the disk
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910694871400448 |
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| author | Zakharov, Dmitrii |
| author_facet | Zakharov, Dmitrii |
| contents | We show that if $A$ is a set of mutually orthogonal exponentials with respect to the unit disk then $|A \cap [-R, R]^2| \lesssim_\varepsilon R^{3/5+\varepsilon}$ holds. This improves the previous bound of $R^{2/3}$ by Iosevich--Kolountzakis. The main new ingredient in the proof is a discretized version of Marstrand's slicing theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14063 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On sets of orthogonal exponentials on the disk Zakharov, Dmitrii Classical Analysis and ODEs Metric Geometry We show that if $A$ is a set of mutually orthogonal exponentials with respect to the unit disk then $|A \cap [-R, R]^2| \lesssim_\varepsilon R^{3/5+\varepsilon}$ holds. This improves the previous bound of $R^{2/3}$ by Iosevich--Kolountzakis. The main new ingredient in the proof is a discretized version of Marstrand's slicing theorem. |
| title | On sets of orthogonal exponentials on the disk |
| topic | Classical Analysis and ODEs Metric Geometry |
| url | https://arxiv.org/abs/2405.14063 |