International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 6, Pages 421-427
Stieltjes transforms on new generalized functions
Department of Mathematical Sciences, Virginia Commonwealth University, Richmond 23284-2014, VA, USA
Received 27 December 1999
Copyright © 2001 John Schmeelk. 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 Stieltjes transform on the equivalence classes of
a new generalized function which has been successfully developed
by Colombeau. Subsets of rapid descent test functions, , as well as tempered distributions, , are used to preserve Fourier analysis techniques.