Inversion theorem for distributional Fourier-Laplace transform

The methods of integral transforms are very efficient to solve and research differential and integral equations of mathematical physics. These methods consist in the integration of an equation with some weight function of two arguments that often results in the simplification of a given initial problem. The main condition for the application of an integral transform is the validity of the inversion theorem which allows one to find an unknown function knowing its image. The aim of the present paper is to provide the generalization of Fourier-Laplace transform in the distributional sense and giving inversion theorem for the distributional Fourier-Laplace transform.