Convolution equations in spaces of distributions supported by cones

Abstract

We describe some examples of surjective convolutors on D ′ ( Γ ) \mathcal {D}’(\Gamma ) , for Γ \Gamma a closed convex cone in R n {{\mathbf {R}}^n} . We also give necessary and suffficient conditions on S 1 , … , S m {S_1}, \ldots ,{S_m} in S ′ ( Γ ) \mathcal {S}’(\Gamma ) to be generators of the whole convolution algebra S ′ ( Γ ) \mathcal {S}’(\Gamma ) .