Fractal uncertainty in higher dimensions

• 成果类型: Article
• 署名作者: Cohen, Alex
• 署名单位: Massachusetts Institute of Technology (MIT)
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X; 1939-8980
• DOI: 10.4007/annals.2025.202.1.4
• 发表日期: 2025-07
• 页码: 265-307
• 关键词: fractal uncertainty principle; plurisubharmonic function; quantum chaos; spectral gaps

摘要

We prove that if a fractal set in Rd 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.