International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 3, Pages 153-158
On the convolution product of the distributional kernel
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Received 18 June 2001; Revised 19 February 2002
Copyright © 2003 A. Kananthai and S. Suantai. 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.
We introduce a distributional kernel which is related to the operator iterated
times and defined by , where is the dimension of the space of the -dimensional Euclidean space, , is a nonnegative integer, and , , , and are complex parameters. It is found that the existence of
the convolution is depending on the conditions of and .