$L^p$ Donoho-Stark Uncertainty Principles for the Dunkl Transform on ${\mathbb{R}^{\text{d}}}$

Abstract

In the Dunkl setting, we establish three continuous uncertainty principles of concentration type, where the sets of concentration are not intervals. The first and the second uncertainty principles are $L^p$ versions and depend on the sets of concentration $T$ and $W$, and on the time function $f$. The time-limiting operators and the Dunkl integral operators play an important role to prove the main results presented in this paper. However, the third uncertainty principle is also $L^p$ version depends on the sets of concentration and he is independent on the band limited function $f$. These uncertainty principles generalize the results obtained for the Fourier transform and the Dunkl transform in the case $p=2$.