Geodesic
The Laplace-Stieltjes transformation on ordered topological vector space of generalized functions
Acta mathematica Universitatis Comenianae, Tome 80 (2011) no. 2 
K. V. Geetha; N. R. Mangalambal. The Laplace-Stieltjes transformation on ordered topological vector space of generalized functions. Acta mathematica Universitatis Comenianae, Tome 80 (2011) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2011_80_2_a8/
@article{AMUC_2011_80_2_a8,
     author = {K. V. Geetha and N. R. Mangalambal},
     title = {The {Laplace-Stieltjes} transformation on ordered topological vector space of generalized functions},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2011},
     volume = {80},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2011_80_2_a8/}
}
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We have combined the Laplace transform and the Stieltjes transform of the form $\hat{f} (x) = \int_0^\infty \frac{f(t)}{(x^m+t^m)^\rho} d t$, $m,\rho>0$ and applied it to an ordered vector space of generalized functions to which the topology of bounded convergence is assigned. Some of the order properties of the transform and its inverse are studied. Also we solve an initial value problem and compare different solutions of the problem.