The Generalized Laplace Transformation of New Spaces of Distributions
by
S. P. Malgonde
Vishwakarma Institute of Technology, 666 Upper Indira Nagar, Pune-411 037 , INDIA
Coauthors: S. R Bandewar

In this paper we introduce new testing function spaces La,b,, Ia,b, and I*a,b, and their corresponding duals. We prove that the above generalized Laplace transformation is an isomorphism between La,b, and Ia,b, for a > 0 and b  R. The generalized Laplace transformation is defined on La,b, and shown that the generalized Laplace transformation is sequential isomorphism between La,b, and (I*a,b, ) when a > 0 and b  R. The definition of the generalized Laplace transformation appears as an extension of a Parseval relation for the classical generalized Laplace transform. To end this paper,we have shown an application of this new transformation thus developed to solve a distributional integral equation in certain spaces La,b, of generalized functions”.

Date received: October 31, 2004