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arXiv · 1712.00281

Left Translates of a Square Integrable Function on the Heisenberg group

R. Radha·Saswata Adhikari
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Abstract

The aim of this paper is to study some properties of left translates of a square integrable function on the Heisenberg group. First, a necessary and sufficient condition for the existence of the canonical dual to a function $\varphi\in L^{2}(\mathbb{R}^{2n})$ is obtained in the case of twisted shift-invariant spaces. Further, characterizations of $\ell^{2}$-linear independence and the Hilbertian property of the twisted translates of a function $\varphi\in L^{2}(\mathbb{R}^{2n})$ are obtained. Later these results are shown in the case of the Heisenberg group.

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R. Radha, Saswata Adhikari. 2017-12-01. Left Translates of a Square Integrable Function on the Heisenberg group. https://arxiv.org/abs/1712.00281

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