Representation Theorem for the Distributional Fourier-Laplace Transform

V. D. Sharma, A. N. Rangari

Abstract: There are many integral transforms including Fourier, Laplace, Mellin, Hankel, Whittaker, Stieltjes, Hilbert, Hartely etc. but the origin of integral transform is Fourier and Laplace transforms. So these two transforms are very important. And this Fourier and Laplace transforms have many applications in various fields like science, physics, mathematics, engineering, geophysics, medical, chemistry, electrical and mechanical separately. In our research we tried to join the Fourier and Laplace transforms and work on it and this resultant Fourier-Laplace transform also may have various applications in some fields of science and technology. The aim of the present paper is to provide the generalization of Fourier-Laplace transform in the distributional sense and giving representation theorem for the distributional Fourier-Laplace transform.

Keywords: Fourier transform, Laplace transform, Fourier- Laplace transform, generalized function, Testing function space