Harmonic analysis on the quaternionic unit ball

In this paper, we will recall the main results of the quaternionic hyperbolic group and the Helgason-Fourier transform on the quaternionic unit ball. We prove then the associated Entropy uncertainty principle. Subsequently, we introduce the notion of the Gabor transform associated to this transform. Finally, we demonstrate certain properties on the Gabor transform and the associated Lieb’s uncertainty principle.