4 papers · 1 filter
Fourier restriction and well-approximable numbers
Robert Fraser, Kyle Hambrook, Donggeun Ryou
We use a deterministic construction to prove the optimality of the exponent in the Mockenhaupt-Mitsis-Bak-Seeger Fourier restriction theorem for dimension and parameter range…
Sharpness of the Mockenhaupt-Mitsis-Bak-Seeger Fourier restriction theorem in all dimensions
Robert Fraser, Kyle Hambrook, Donggeun Ryou
We prove the optimality of the exponent in the Mockenhaupt-Mitsis-Bak-Seeger Fourier restriction theorem in all dimensions and the full parameter range . Our const…
Fourier decay of measures supported on sets of numbers with consecutive partial quotients belonging to a given set
Robert Fraser
We consider measures supported on sets of irrational numbers possessing many consecutive partial quotients satisfying a condition based on the previous partial quotients. We show t…
Sharp Fourier decay estimates for measures supported on the well-approximable numbers
Robert Fraser, Thanh Nguyen
We construct a measure on the well-approximable numbers whose Fourier transform decays at a nearly optimal rate. This gives a logarithmic improvement on a previous construction of…