On the inversion of the Laplace transform by the use of a regularized displacement operator

We develop a numerical method for approximating f, given its Laplace transform g on (0, infinity), i.e. integral(0)(infinity)f(t)e(-st) dt = g(s) assuming that g is in L-2(0, infinity). The method is based on the Tichonov regularization operator. This operator is approximated by a finite-dimensional displacement operator. Convergence of the method, together with some examples, will be given.