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On sets of orthogonal exponentials on the disk
Published 22 May 2024 in math.CA and math.MG | (2405.14063v2)
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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