Spherical Fourier transform on the quaternionic Heisenberg group

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’.

Keywords:

• Quaternionic Heisenberg group
• Fourier transform
• spherical Fourier transform
• spherical function

2010 Mathematics Subject Classifications:

• 43A90
• 26A33
• 44-XX
• 33-XX

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).