Bounded spherical functions and Heisenberg inequality on quaternionic Heisenberg group

摘要

In this paper, we will construct the bounded spherical functions of the quaternionic Heisenberg group using the theory of representations of the semi-direct product of H-q and the subgroup K of the quaternions of module 1. Finally, we prove the Heisenberg inequality for the spherical Fourier transform and the spherical Gabor transform on the Quaternionic Heisenberg group.