Hardy's Theorem for Gabor transform

Abstract

We establish analogues of Hardy's theorem for Gabor transform on locally compact abelian groups, Euclidean motion group and several general classes of nilpotent Lie groups which include Heisenberg groups, thread-like nilpotent Lie groups, $2$-NPC nilpotent Lie groups and low-dimensional nilpotent Lie groups.

This paper has been withdrawn by the author as there are some gaps in a proof