International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 2, Pages 275-282
doi:10.1155/S0161171291000315
A note on the convolution and the product in D′ and S′
A. Kamiński
and R. Rudnicki
Institute of Mathematics, Polish Academy of Sciences, Wieczorka 8, Katowice 40-013, Poland
Abstract
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.