Geodesic
Tauberian theorems with a remainder for Laplace transforms in the plane
Sbornik. Mathematics, Tome 46 (1983) no. 3, pp. 417-428

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General theorems are proved that for certain classes of (complex-valued) functions $f(v)$ enable us to find an asymptotic expansion of $f$ as $v\to+\infty$ from an asymptotic expansion of its Laplace transform $g(s)=\displaystyle\int_0^\infty f(v)e^{-vs}\,dv$ (as $s\to 0$) with respect to a domain having the origin of coordinates as an adherent point. A number of previous results are obtained as special cases. Bibliography: 3 titles. 
@article{SM_1983_46_3_a6,
     author = {V. I. Mel'nik},
     title = {Tauberian theorems with a remainder for {Laplace} transforms in the plane},
     journal = {Sbornik. Mathematics},
     pages = {417--428},
     publisher = {mathdoc},
     volume = {46},
     number = {3},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_46_3_a6/}
}
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V. I. Mel'nik. Tauberian theorems with a remainder for Laplace transforms in the plane. Sbornik. Mathematics, Tome 46 (1983) no. 3, pp. 417-428. http://geodesic.mathdoc.fr/item/SM_1983_46_3_a6/