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In this paper Gabor system of certain type based on the unitary dual of theHeisenberg group $\mathbb{H}^n$ is introduced and a sufficient condition isobtained for the Gabor system to be a Bessel sequence for$L^2(\mathbb{R}^*,\mathcal{B}_2;d\kappa)$ using the $Schr\"{o}dinger$representation of $\mathbb{H}^n$, where $\mathcal{B}_2$ denotes the class ofHilbert-Schmidt operators on $L^2(\mathbb{R}^n)$ and $d\kappa$ denotes the Haarmeasure on $\mathbb{R}^*$. Further a necessary and sufficient condition isprovided for the Gabor system to be an orthonormal system, a Parseval framesequence, a frame sequence and a Riesz sequence.

Gabor System Based on the Unitary Dual of the Heisenberg Group