Convolution Equations in Spaces of Distributions Supported by Cones

Abstract

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

Locations

• Proceedings of the American Mathematical Society - View - PDF