Sharp Fourier decay estimates for measures supported on the well-approximable numbers

2024/09/04 by Robert Fraser, Thanh Nguyen, Fraser, Robert +1
Mathematics · #42A99 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2409.02854

openalex publication_date 2024/09/04 · openalex created_date 2024/10/06 · openalex updated_date 2026/07/28

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.

Related

• Fourier decay of measures supported on sets of numbers with consecutive partial quotients belonging to a given set
• Average decay of the Fourier transform of measures with applications
• Fourier decay for self-similar measures
• Fourier decay of self-similar measures on the complex plane
• Fourier decay rate of coin-tossing type measures