Geodesic
Analogues of Tauberian theorems for the Laplace transform
Izvestiya. Mathematics , Tome 66 (2002) no. 6, pp. 1219-1242

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We present various strengthened versions of the Tauberian theorem for the Laplace transform proved by S. V. Konyagin and A. Yu. Popov in 1995. 
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     author = {A. Yu. Popov and Yu. S. Chainikov},
     title = {Analogues of {Tauberian} theorems for the {Laplace} transform},
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     number = {6},
     year = {2002},
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A. Yu. Popov; Yu. S. Chainikov. Analogues of Tauberian theorems for the Laplace transform. Izvestiya. Mathematics , Tome 66 (2002) no. 6, pp. 1219-1242. http://geodesic.mathdoc.fr/item/IM2_2002_66_6_a5/