Convolution Theorem for Distributional Fourier-Laplace Transform

In the tremendous expanding knowledge of science, mathematics plays a vital role. In the words of Philip, Mathematics is a science of quantity and space. Especially in quantum field theory, field of partial differential equations, Harmonic analysis etc. the notion of generalized functions is very essential. The convolution theorem of the transform plays an important role in digital signal processing. The usefulness of convolution theorem can be best explained by its application in filtering. This paper is concerned with the generalization of Fourier-Laplace transform in the distributional sense. The main aim of this paper is to prove the properties of convolution and Convolution theorem for Fourier-Laplace transform.