Theorems of Chernoff and Ingham for certain eigenfunction expansions

Abstract

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 ${\mathbb{R}}^n.$

The title has been changed. 25pages. Accepted for publication in Advances in Mathematics