Abstract
In this paper, we introduce the definitions of the Fourier transform and spherical Fourier transform on quaternionic Heisenberg group, then we present some of their properties, in particular, we will determine the spherical functions and the heat kernel of quaternionic Heisenberg group. Finally, we prove a qualitative uncertainty principle ‘Donoho–Stark's uncertainty principle’.
Acknowledgments
The authors are grateful to the referees for carefully reading the paper and for elaborate and valuable suggestions and comments.
Disclosure statement
No potential conflict of interest was reported by the author(s).