Generalization of Fourier-Laplace Transforms

The Laplace transform is a widely used integral transform with many applications in physics and engineering. The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes of vibration, the Laplace transform resolves a function into its moments. Like the Fourier transform, The Laplace transform is used for solving differential and integral equations. This paper discusses an extension of Fourier –Laplace transform in the distributional generalized sense. The Twelve testing function space are defined by using Gelfand – Shilove technique. The paper describes the topological properties of S – type spaces for distributional Fourier – Laplace transform and also the results on strict inductive limit spaces.