Fourier restriction and well-approximable numbers
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866908422008471552 |
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| author | Fraser, Robert Hambrook, Kyle Ryou, Donggeun |
| author_facet | Fraser, Robert Hambrook, Kyle Ryou, Donggeun |
| contents | 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 Łaba \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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09463 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fourier restriction and well-approximable numbers Fraser, Robert Hambrook, Kyle Ryou, Donggeun Classical Analysis and ODEs 42A38, 28A78, 28A80, 11J83 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 Łaba \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. |
| title | Fourier restriction and well-approximable numbers |
| topic | Classical Analysis and ODEs 42A38, 28A78, 28A80, 11J83 |
| url | https://arxiv.org/abs/2311.09463 |