Year: 2025
Type: article
Abstract: We prove that if a fractal set in $\mathbb{R}^d$ avoids lines in a certain quantitative sense, which we call line porosity, then it has a fractal uncertainty principle. The main ingredient is a new higher-dimensional Beurling--Malliavin multiplier theorem.
Source: Annals of Mathematics
Author: Alex Cohen
Institution: Massachusetts Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4411992245