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Representation Theories for the Laplace Transform
Canadian mathematical bulletin, Tome 10 (1967) no. 3, pp. 333-345

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The Widder-Post real inversion operator [4[ is defined by 1.1 k = 1, 2,.... Utilizing this inversion operator one can obtain the following representation theorem (see e.g. [4[ Chapter VII, Theorem 15a). 
Heinig, H. P. Representation Theories for the Laplace Transform. Canadian mathematical bulletin, Tome 10 (1967) no. 3, pp. 333-345. doi: 10.4153/CMB-1967-030-4
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     title = {Representation {Theories} for the {Laplace} {Transform}},
     journal = {Canadian mathematical bulletin},
     pages = {333--345},
     year = {1967},
     volume = {10},
     number = {3},
     doi = {10.4153/CMB-1967-030-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-030-4/}
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