Convergence rate of Post-Widder approximate inversion of the Laplace transform (Q1593693)

The authors obtain the convergence rate of the Post-Widder approximate inversion of the Laplace transform in \(L_2(R_+)\) at two assumptions on the regularity of the original function \(f(t)\). Such an inversion should be applied if the image function \(F(p)\) is known only on the positive axis \(R_+\). The method is based on the presentation of the Laplace transform via the Parseval formula for the Mellin convolution.