p. 243 - 249 The Laplace-Stieltjes transformation on ordered topological vector space of generalized functions
K. V. Geetha and N. R. Mangalambal Received: November 15, 2010;
Accepted: January 12, 2011
Abstract.
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.
Keywords:
Laplace-Stieltjes transformation; positive cone; orderbounded
AMS Subject classification:
Primary: 46F10
Secondary: 46A04, 46A08
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