Unique continuation inequalities for the Dunkl-Schrödinger equation via uncertainty principles

In this paper, we establish unique continuation inequalities at two time points for the Dunkl–Schrödinger 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–Schrödinger equation.