PRINCIPAL OF NILPOTENT LIE GROUPS

Abstract

We prove Hardy’s type uncertainty principle on connected nilpotent Lie groups for the Fourier transform. An analogue of Hardy’s theorem for the Gabor transform has been established for connected and simply connected nilpotent Lie groups. Finally Beurling’s theorem for the Gabor transform is discussed for groups of the form Rn ×K, where K is a compact group.