The failure of the fractal uncertainty principle for the Walsh--Fourier transform

Abstract

We construct $\delta$-regular sets with $\delta \ge \frac{1}{2}$ for which the analog of the Bourgain--Dyatlov Fractal Uncertainty Principle fails for the Walsh--Fourier transform.

arXiv commentThis version incorporates referee's comments. Most notable change is the inclusion of Lemma 4.8