ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXX, 2 (2011)
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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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

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