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 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2011, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |