Explicit Salem sets in $\mathbb{R}^n$
Classical Analysis and ODEs
2020-09-07 v2
Abstract
We construct the first explicit (i.e., non-random) examples of Salem sets in 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.
Keywords
Cite
@article{arxiv.1909.04581,
title = {Explicit Salem sets in $\mathbb{R}^n$},
author = {Robert Fraser and Kyle Hambrook},
journal= {arXiv preprint arXiv:1909.04581},
year = {2020}
}
Comments
18 pages