Hardy's Uncertainty Principle for Lie Groups

A classical theorem due to Hardy says that a non-zero measurable function on the real line and irs Fourier transform cannot both have very strong exponential decay. Hardy's theorem also holds for Rⁿ, and during the past ten years there has been much effort to prove Hardy-like theorems for various classes of connected Lie groups. Specifically, analogues of Hardy's theorem have been established for motion groups, non-compact connected semisimple Lie groups with finite centre and simply connected nilpotent Lie groups. The talk will survey these results and finally focus on recent work on non-simply connected nilpotent Lie groups.