Unique continuation inequalities for the Dunkl-Schr\"odinger equation via uncertainty principles
Analysis of PDEs
2026-05-19 v1
Abstract
In this paper, we establish unique continuation inequalities at two time points for the Dunkl--Schr\"odinger equation. The proof is based on quantitative uncertainty principles for the Dunkl transform. In particular, we prove that pairs of (\varepsilon,k)-thin sets form strong annihilating pairs for the Dunkl transform, which yields quantitative unique continuation properties for solutions to the Dunkl--Schr\"odinger equation.
Keywords
Cite
@article{arxiv.2605.18021,
title = {Unique continuation inequalities for the Dunkl-Schr\"odinger equation via uncertainty principles},
author = {Xingyu Zhao and Hui Xu and Zhiwen Duan},
journal= {arXiv preprint arXiv:2605.18021},
year = {2026}
}