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Inversion Theorems for the Laplace-Stieltjes Transform
Published online by Cambridge University Press: 20 November 2018
Extract
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.
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- Copyright © Canadian Mathematical Society 1966