Bounded spherical functions and Heisenberg inequality on quaternionic Heisenberg group (Q2129654)

The authors prove the Heisenberg inequality for the spherical Fourier transform and the spherical Gabor transform on the quaternionic Heisenberg group. On the way, they give an alternate description of the bounded spherical functions of the quaternionic Heisenberg group using the theory of representations of the semi-direct product of groups, which is a well-known method. The major part of the paper is based on already known results and estimates. Some results on a similar theme can be found in, e.g., work by \textit{F.~Zhu} [Pac. J. Math. 209, No.~1, 175--199 (2003; Zbl 1054.43009)], \textit{M.~Christ} et al. [Nonlinear Anal., Theory Methods Appl., Ser.~A, Theory Methods 130, 361--395 (2016; Zbl 1329.26028)] amongst others.