Sbornik. Mathematics, Tome 46 (1983) no. 3, pp. 417-428
Citer cet article
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/
@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},
year = {1983},
volume = {46},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1983_46_3_a6/}
}
TY - JOUR
AU - V. I. Mel'nik
TI - Tauberian theorems with a remainder for Laplace transforms in the plane
JO - Sbornik. Mathematics
PY - 1983
SP - 417
EP - 428
VL - 46
IS - 3
UR - http://geodesic.mathdoc.fr/item/SM_1983_46_3_a6/
LA - en
ID - SM_1983_46_3_a6
ER -
%0 Journal Article
%A V. I. Mel'nik
%T Tauberian theorems with a remainder for Laplace transforms in the plane
%J Sbornik. Mathematics
%D 1983
%P 417-428
%V 46
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1983_46_3_a6/
%G en
%F SM_1983_46_3_a6
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.
