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arXiv · 2405.14063

On sets of orthogonal exponentials on the disk

Dmitrii Zakharov
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Abstract

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.

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Dmitrii Zakharov. 2024-05-22. On sets of orthogonal exponentials on the disk. https://arxiv.org/abs/2405.14063

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