Variations on a theorem of cowling and price with applications to nilpotent Lie groups

Abstract

In this paper we prove a new version of the Cowlin-Price theorem for Fourier transforms on Rⁿ. Using this we formulate and prove an uncertainty principle for operators. This leads to an analogue of the Cowling-Price theorem for nilpotent Lie groups. We also prove an exact analogue of the Cowling-Price theorem for the Heisenberg group.