  We prove an uncertainty principle for certain eigenfunction expansions on $
L^2(\mathbb{R}^+,w(r)dr) $ and use it to prove analogues of theorems of
Chernoff and Ingham for Laplace-Beltrami operators on compact symmetric spaces,
special Hermite operator on $ \mathbb{C}^n $ and Hermite operator on $
\mathbb{R}^n.$
