  Hardy's type uncertainty principle on connected nilpotent Lie groups for the
Fourier transform is proved. An analogue of Hardy's theorem for Gabor transform
has been established for connected and simply connected nilpotent Lie groups.
Finally Beurling's theorem for Gabor transform is discussed for groups of the
form $\mathbb{R}_n \times K$, where $K$ is a compact group

Representation Theory