Let $G $ be a noncompact semisimple Lie group with finite centre. Let $X=G/K$ be the associated Riemannian symmetric space and assume that $X$ is of rank one. The spectral projections associated to the Laplace-Beltrami operator are given by $P_{ \lambda}f =f\ast \Phi_{ \lambda}$, where $\Phi_{ \lambda}$ are the elementary spherical functions on $X$. In this paper, we prove an Ingham type uncertainty principle for $P_{ \lambda}f$. Moreover, similar results are obtained in the case of spectral projections associated to Dunkl Laplacian.
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