A note on the convolution and the product in D′ and S′
Andrzej Kamiński, RYSZARD M. RUDNICKI · International Journal of Mathematics and Mathematical Sciences · 1990
Examples of tempered distibutions are shown such that the convolution and product exist in D′ and are tempered distributions, but they do not exist in S′. On the other hand, there exist tempered distributions whose convolution or product exist in D′ but are not tempered distributions.