  Let $C$ denote a closed convex cone $C$ in $\mathbb{R}^d$ with apex at 0. We
denote by $\mathcal{E}'(C)$ the set of distributions having compact support
which is contained in $C$. Then $\mathcal{E}'(C)$ is a ring with the usual
addition and with convolution. We give a necessary and sufficient analytic
condition on $\hat{f}_1,..., \hat{f}_n$ for $f_1,...,f_n \in \mathcal{E}'(C)$
to generate the ring $\mathcal{E}'(C)$. (Here $\hat{\cdot}$ denotes
Fourier-Laplace transformation.) This result is an application of a general
result on rings of analytic functions of several variables by H\"ormander. En
route we answer an open question posed by Yutaka Yamamoto.
