Sharp Fourier decay estimates for measures supported on the well-approximable numbers
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Authors
Fraser, Robert
Nguyen, Thanh
Advisors
Issue Date
2025-08-25
Type
Article
Keywords
Harmonic analysis , Geometric measure theory , Diophantine approximation , Hausdorff dimension
Citation
Fraser, R., & Nguyen, T. (2025). Sharp Fourier decay estimates for measures supported on the well-approximable numbers. Annales Fennici Mathematici, 50(2). https://doi.org/10.54330/afm.163951
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.
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Publisher
Finnish Mathematical Society
Journal
Annales Fennici Mathematici
Book Title
Series
PubMed ID
ISSN
27370690