R. Radha, Saswata Adhikari
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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