Bounded spherical functions and Heisenberg inequality on quaternionic Heisenberg group

Bounded spherical functions and Heisenberg inequality on quaternionic Heisenberg group

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 transfo...

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Veröffentlicht in:Advances in operator theory 2022-04, Vol.7 (2), Article 24
Hauptverfasser: Amghar, Walid, Fahlaoui, Said
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
Operator Theory
Original Paper
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Zusammenfassung: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.
ISSN:2662-2009
2538-225X
DOI:10.1007/s43036-022-00188-z