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arXiv · 2311.09463

Fourier restriction and well-approximable numbers

Robert Fraser·Kyle Hambrook·Donggeun Ryou
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Abstract

We use a deterministic construction to prove the optimality of the exponent in the Mockenhaupt-Mitsis-Bak-Seeger Fourier restriction theorem for dimension $d=1$ and parameter range $0 < a,b \leq d$ and $b\leq 2a$. Previous constructions by Hambrook and {\L}aba \cite{HL2013} and Chen \cite{chen} required randomness and only covered the range $0 < b \leq a \leq d=1$. We also resolve a question of Seeger \cite{seeger-private} about the Fourier restriction inequality on the sets of well-approximable numbers.

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Robert Fraser, Kyle Hambrook, Donggeun Ryou. 2023-11-15. Fourier restriction and well-approximable numbers. https://arxiv.org/abs/2311.09463

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