2 problems

Let $S$ be a non-negative non-decreasing function whose Mellin transform … after subtraction of the pole term $A/(s-1)$ admits an analytic extension to a half-plane…

Let $S$ be non-decreasing on $[0,infty)$, and suppose that its Laplace-Stieltjes transform satisfies … Assume this function extends analytically to the half-plane…