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
Received 27 November 1989; Revised 3 March 1990

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.