A Study of Laplace-Carson Transform and Its Associated Space of Distribution

The integral transforms are essential tools that offer powerful methods for simplifying problems across engineering, physics, and applied mathemat- ics.This paper explores the Laplace -Carson transform within the framework of distribution theory.We have developed the new test function space W and its dual W We have established fundamental existence and uniqueness theo-rem.Furthermore,we have proved the convolution theorem and theorem related to derivative of distributions in W′.Finally, we have tried to illustrate som examples of regular and singular distributions in W′.