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

## TL;DR

This paper establishes necessary and sufficient conditions for sampling and reconstruction of functions in shift-invariant subspaces of L^2 on the Heisenberg group, extending classical results to a non-commutative setting.

## Contribution

It provides a comprehensive framework for sampling and reconstruction in the Heisenberg group, generalizing classical theorems to this non-commutative context.

## Key findings

- Derived conditions for sampling in the Heisenberg group
- Established reconstruction formulas for shift-invariant subspaces
- Extended classical sampling theorems to a non-commutative setting

## Abstract

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