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arXiv · 2211.10240

Systems of Left Translates and Oblique Duals on the Heisenberg Group

S. R. Das·P. Massopust·R. Radha
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Abstract

In this paper, we characterize the system of left translates $\{L_{(2k,l,m)}g:k,l,m\in\mathbb{Z}\}$, $g\in L^2(\mathbb{H})$, to be a frame sequence or a \emph{Riesz} sequence in terms of the twisted translates of the corresponding function $g^\lambda$. Here, $(\mathbb{H}$ denotes the Heisenberg group and $g^\lambda$ the inverse Fourier transform of $g$ with respect to the central variable. This type of characterization for a \emph{Riesz} sequence allows us to find some concrete examples. We also study the structure of the oblique dual of the system of left translates $\{L_{(2k,l,m)}g:k,l,m\in\mathbb{Z}\}$ on $(\mathbb{H}$. This result is also illustrated with an example.

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BibTeXRIS

S. R. Das, P. Massopust, R. Radha. 2022-11-18. Systems of Left Translates and Oblique Duals on the Heisenberg Group. https://arxiv.org/abs/2211.10240

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