Inversion Theorems for the Laplace-Stieltjes Transform
Zeev Ditzian, A. Jakimovski · Canadian Journal of Mathematics · 1966
The Laplace-Stieltjes transform f(x) of the function α(t) is denned by 1 where α(t) is a function of bounded variation in each closed interval [0, R] (R > 0) and the right-hand side of (1) is supposed to be convergent for some x = X0. The Laplace transform f(x) of the function ϕ(t) is defined by 2 where ϕ(t) ∈ L1(0, R) for each R > 0 and the right-hand side of (2) is supposed to be convergent for some x = x0.