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The paper deals with the necessary and sufficient conditions for obtainingreconstruction formulae and sampling theorems for every function belonging tothe principal shift invariant subspace of $L^2(\mathbb{H}^n)$, both in the timedomain and a transform domain, where $\mathbb{H}^n$ denotes the Heisenberggroup.

Sampling theorem and reconstruction formula for the space of translates on the Heisenberg group