Geodesic
Inversion Theorems for the Laplace-Stieltjes Transform
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 503-516

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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) ∈ L 1(0, R) for each R > 0 and the right-hand side of (2) is supposed to be convergent for some x = x0. 
Ditzian, Z.; Jakimovski, A. Inversion Theorems for the Laplace-Stieltjes Transform. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 503-516. doi: 10.4153/CJM-1966-050-x
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