The Cowling-Price theorem for semisimple Lie groups

Abstract

M. G. Cowling and J. F. Price showed a generalization of Hardy’s theorem as follows. If v and w grow very rapidly, then the finiteness of kvf kp and kwf kq implies that f 1⁄4 0, where f denotes the Fourier transform of f . We give an analogue of this theorem for the Helgason–Fourier transform for homogeneous vector bundles over Riemannian symmetric spaces and for connected noncompact semisimple Lie groups with finite centre.