Generators for rings of compactly supported distributions

Details Generators for rings of compactly supported distributions Generators for rings of compactly supported distributions

2010-04-06

arxiv.org/abs/1004.0927v1

Integral Equations Operator Theory 69 (2011), no. 1, 63-71

Mathematics

Functional Analysis

9 pages

Scientific paper

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.

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