Sharp Fourier decay estimates for measures supported on the well-approximable numbers | Synapse
August 25, 2025Open Access
Sharp Fourier decay estimates for measures supported on the well-approximable numbers
Key Points
The constructed measure exhibits optimal decay behavior of its Fourier transform, improving upon prior work.
This new measure's Fourier transform decays logarithmically faster than earlier constructions by Kaufman.
The approach taken focuses on establishing decay estimates for measures on well-approximable numbers.
The findings highlight the potential for enhancements in understanding measures and Fourier transforms in mathematical analysis.
Abstract
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 Kaufman.