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Fourier restriction and well-approximable numbers
Fraser, Robert Hambrook, Kyle Ryou, Donggeun
Fraser, Robert
Hambrook, Kyle
Ryou, Donggeun
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2024-11-01
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Article
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Mathematics,Fourier restriction
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Fraser, R., Hambrook, K. & Ryou, D. Fourier restriction and well-approximable numbers. Math. Ann. (2024). https://doi.org/10.1007/s00208-024-03000-w
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≤d and b≤2a. Previous constructions by Hambrook and Łaba [15] and Chen [5] required randomness and only covered the range 0<b≤a≤d=1. We also resolve a question of Seeger [29] about the Fourier restriction inequality on the sets of well-approximable numbers. © The Author(s) 2024.
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Springer Science and Business Media Deutschland GmbH
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Mathematische Annalen
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00255831