A GENERALIZATION OF LAPLACE AND FOURIER TRANSFORMS
NIKOLAOS HALIDIAS *
Department of Mathematics, University of the Aegean, karlovassi, Samos, 83200, Greece.
*Author to whom correspondence should be addressed.
Abstract
In this note we propose a generalization of the Laplace and Fourier transforms which we call symmetric Laplace transform. It combines both the advantages of the Fourier and Laplace transforms. We give the definition of this generalization, some examples and basic properties. We also give the form of its inverse by using the theory of the Fourier transform. Finally, we apply the symmetric Laplace transform to a parabolic problem and to an ordinary differential equation.
Keywords: Fourier transform, Laplace transform, functions of exponential order