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arXiv · 2105.12961

Gabor System Based on the Unitary Dual of the Heisenberg Group

S. R. Das·R. Radha
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Abstract

In this paper Gabor system of certain type based on the unitary dual of the Heisenberg group $\mathbb{H}^n$ is introduced and a sufficient condition is obtained for the Gabor system to be a Bessel sequence for $L^2(\mathbb{R}^*,\mathcal{B}_2;dκ)$ using the $Schrödinger$ representation of $\mathbb{H}^n$, where $\mathcal{B}_2$ denotes the class of Hilbert-Schmidt operators on $L^2(\mathbb{R}^n)$ and $dκ$ denotes the Haar measure on $\mathbb{R}^*$. Further a necessary and sufficient condition is provided for the Gabor system to be an orthonormal system, a Parseval frame sequence, a frame sequence and a Riesz sequence.

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S. R. Das, R. Radha. 2021-05-27. Gabor System Based on the Unitary Dual of the Heisenberg Group. https://arxiv.org/abs/2105.12961

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