International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 3, Pages 441-458
doi:10.1155/S016117127900034X
The stieltjes transform of distributions
1Department of Mathematics, John Abbott College, Montreal, Canada
2Department of Mathematics, Carleton University, Ottawa, Canada
Received 28 September 1978; Revised 3 April 1979
Copyright © 1979 U. N. Tiwari and J. N. Pandey. 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
In the present work, two complex inversion formulas of Byrne and Love for generalized Stieltjes transformation are shown to be valid for a class of distributions. This is accomplished by transfering the complex inversion formulas on the testing function space of a class of distributions and then showing that the limiting process in the resulting formula converges in the topology of the testing function space.