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

Stieltjes transforms on new generalized functions

Department of Mathematical Sciences, Virginia Commonwealth University, Richmond 23284-2014, VA, USA

Received 27 December 1999

Copyright © 2001 Hindawi Publishing Corporation. 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.

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