  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.
