If µ is a compactly supported distribution on the n-dimensional Euclidean space, the convolution operator Cµ: f→ f ∗ µ is well defined as a map from the space of smooth functions to itself. Then we arrive at the following question. When is Cµ surjective? Ehrenpreis gave an answer to this question by showing that Cµ is surjective if and only if the Fourier-Laplace transform of µ is slowly decreasing. In this talk, we start with the above result by Ehrenpreis, and next, we explain that an analogous result holds for convolution operators on noncompact symmetric spaces.