Tauberian theorems with a remainder for Laplace transforms in the plane

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.
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