Long Wei

Observability Inequalities and the Logvinenko--Sereda Theorem for the Dunkl Transform

Let $R$ be a normalized root system in $\mathbb{R}^d$ with reflection group $G$, let $k$ be a $G$-invariant multiplicity function, and let $\mathcal{F}_k$ be the associated Dunkl transform. We write $k_\alpha=k(\alpha)>0$ and $\mathrm{d}\mu_k(x)=w(x)\,\mathrm{d}x$, where $w(x)=\prod_{\alpha\in R_+}|\langle x,\alpha\ran...