International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 3, Pages 425-432

Iterated Stieltjes transform of generalized functions

L. S. Dube

Department of Mathematics, Vanier College, Montreal, Canada

Received 20 March 1984

Copyright © 1985 L. S. Dube. 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.


The generalized S2-transform of a member of f of a certain space of generalized functions is defined as F(x)=f(t),k(x,t;ρ), wherek(x,t;ρ)=01(x+y)ρ(y+t)ρ  dy,  ρ>12,0<x<  and  0<t<. An inversion theorem for the transform is established interpreting the oonvergene in the weak distributional sense.