Optimal Tauberian constant in Ingham's theorem for Laplace transforms

Gregory Debruyne, Jasson Vindas

It is well known that there is an absolute constant $\mathfrak{C}>0$ such that if the Laplace transform $G(s)={\int }_0^{\infty }\rho (x)e^{-sx}\mathrm{d}x$ of a bounded function $\rho$…