Direct regularization of the inversion of real-valued Laplace transforms

The paper presents a regularization method for the inversion of real-valued Laplace transforms. A regularizing inverse Laplace operator is obtained for a subspace of Laplace transforms directly from the Laplace transformation definition. The fact that a regularized solution converges to the exact one when input data inaccuracy tends to zero is proven. Error analysis based on an analytical link between the regularized and exact solutions is given. This error analysis reflects some general limitations for any method of inversion of real-valued Laplace transforms. The numerical results are briefly discussed.