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.