An abstract uncertainty principle with applications
Abstract
Under Wigdersons' framework and by sorting out the technical points in the recent works of Tang (J. Fourier Anal. Appl. 31 (2025)) and Dias-Luef-Prata (J. Math. Pures Appl. (9) 198 (2025)), we prove an abstract uncertainty principle for functions in the setting. An immediate consequence is a new uncertainty principle for the Fourier transform, unifying and extending many existing results. More applications are shown for PDEs, including the moment growth estimates for some linear and nonlinear dispersive equations, and a type of weighted lower bound estimate for the spacetime moment of the Schr\"{o}dinger equation and heat equation inspired by the control theory.
Cite
@article{arxiv.2504.04345,
title = {An abstract uncertainty principle with applications},
author = {Tianxiao Huang and Ze Li and Jiani Liu},
journal= {arXiv preprint arXiv:2504.04345},
year = {2025}
}
Comments
We have corrected a mistake in Theoreom 1.12 in the earlier version, and we thank Prof. Nicolas Burq for pointing out the mistake