ABOUT THE EQUALITY OF THE TRANSFORM OF LAPLACE TO THE TRANSFORM OF FOURIER

Abstract

We proved that the transform of Laplace does not have complex part on the complex axis for the wide class of functions in different situations. The main theorem is proved presenting a function as sum of two Laplace transforms. The transforms are defined in the left and right parts of the plain accordingly. Such presentation is proved to be unique. With help of the results we obtain equality of the transforms of Laplace and Fourier for some class of functions.

Keywords

• Laplace transform
• Fourier transforms
• Dirichlet problem