Fourier restriction and well-approximable numbers
- Resource Type
- Working Paper
- Authors
- Fraser, Robert; Hambrook, Kyle; Ryou, Donggeun
- Source
- Subject
- Mathematics - Classical Analysis and ODEs
42A38, 28A78, 28A80, 11J83
- Language
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 Laba and Chen required randomness and only covered the range $0 < b \leq a \leq d=1$. We also resolve a question of Seeger about the Fourier restriction inequality on the sets of well-approximable numbers.
Comment: 27 Pages