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Explicit Salem sets in $\mathbb{R}^n$

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arxiv 1909.04581 v2 pith:IQABEVI2 submitted 2019-09-10 math.CA

Robert Fraser , Kyle Hambrook This is my paper · ORCID
classification math.CA
keywords explicitmathbbsalemsetsapproximationarbitrarycompletelyconstruct
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abstract

We construct the first explicit (i.e., non-random) examples of Salem sets in $\mathbb{R}^n$ of arbitrary prescribed Hausdorff dimension. This completely resolves a problem proposed by Kahane more than 60 years ago. The construction is based on a form of Diophantine approximation in number fields.

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  1. Sharpness of the Mockenhaupt-Mitsis-Bak-Seeger Fourier restriction theorem in all dimensions

    math.CA 2025-05 conditional novelty 8.0 of 10

    The Mockenhaupt-Mitsis-Bak-Seeger restriction exponent is optimal for all d and all 0<a,b<d, via deterministic Salem set constructions.

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