Sharp Fourier decay estimates for measures supported on the well-approximable numbers
Fraser, Robert Nguyen, Thanh
Fraser, Robert
Nguyen, Thanh
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2025-08-25
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Article
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Harmonic analysis,Geometric measure theory,Diophantine approximation,Hausdorff dimension
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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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Finnish Mathematical Society
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Annales Fennici Mathematici
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27370690