Explicit Salem Sets in ${\mathbb{R}}^2$

Abstract

We construct explicit (i.e., non-random) examples of Salem sets in ${\mathbb{R}}^2$ of dimension $s$ for every $0\le s\le 2$. In particular, we give the first explicit examples of Salem sets in ${\mathbb{R}}^2$ of dimension $0<s<1$. This extends a theorem of Kaufman.

References in corpus (1)

• Arithmetic progressions in sets of fractional dimension