International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 2, Pages 275-282

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

Received 27 November 1989; Revised 3 March 1990

Copyright © 1991 A. Kamiński and R. Rudnicki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.