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On representations, inversions, and approximations of Laplace transforms in Banach spaces. (English) Zbl 0791.44002
The paper extends the basic results of the classical Laplace transform to the Laplace transform of bounded Bochner integrable functions and the Laplace-Stieltjes transform of Lipschitz continuous functions with values in a Banach space. These results concern the existence, the analyticity, Widder’s representation theorem, the Post-Widder inversion formula, the complex inversion formula, and some approximation theorems.
Reviewer: L.Berg (Rostock)

MSC:
44A10 Laplace transform
45P05 Integral operators
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