Abstract
In this paper, we study some operator theoretical properties of pseudo-differential operators with operator-valued symbols on the Heisenberg motion group. Specifically, we investigate –
boundedness of pseudo-differential operators on the Heisenberg motion group for the range
. We also provide a necessary and sufficient condition on the operator-valued symbols in terms of λ-Weyl transforms such that the corresponding pseudo-differential operators on the Heisenberg motion group are in the class of Hilbert–Schmidt operators. As a consequence, we obtain a characterization of the trace class pseudo-differential operators on the Heisenberg motion group and provide a trace formula for these trace class operators.
2010 Mathematics Subject Classifications:
Acknowledgments
The authors would like to thank an anonymous referee for valuable suggestions which improved the presentation of this paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Data availability statement
The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials.