International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 6, Pages 421-427
doi:10.1155/S0161171201004252

Stieltjes transforms on new generalized functions

Abstract

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, 𝒮(ℝn), as well as tempered distributions, 𝒮′(ℝn), are used to preserve Fourier analysis techniques.