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.
Categories: math.FA math.OC math.RA