Let $\mathcal{E}'(\mathbb{R})$ be equipped with its usual strong topology (being the dual space of $\mathcal{E}(\mathbb{R})$). Is convolution jointly continuous on $\mathcal{E}'(\mathbb{R})$?



Is convolution jointly continuous on $\mathcal{E}'$?
Yes. This is Théorème IV in §3 of Chapitre VI (page 157) in Laurent Schwartz's *Théorie des distributions*.


