Geodesic
Asymptotic Estimates of Functions Based on the Behavior of Their Laplace Transforms near Singular Points
Matematičeskie zametki, Tome 93 (2013) no. 6, pp. 920-931

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This paper deals with the relationship between the behavior of a real function $\nu(t)$ as $t\to +\infty$ and the behavior of the Laplace transform $F[\nu](s)$ of the charge $d\nu(t)$, $$ F[\nu](s)=\int_0^{\infty}e^{-st}\,d\nu(t), $$ near its singular point.
Mots-clés : Laplace transform
Keywords: nonmonotone real function, oscillation of a function, Riemann zeta-function, Dirichlet integral, Tauberian theorem, charge, measure. 
@article{MZM_2013_93_6_a9,
     author = {O. A. Petruschov},
     title = {Asymptotic {Estimates} of {Functions} {Based} on the {Behavior} of {Their} {Laplace} {Transforms} near {Singular} {Points}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {920--931},
     publisher = {mathdoc},
     volume = {93},
     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_6_a9/}
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O. A. Petruschov. Asymptotic Estimates of Functions Based on the Behavior of Their Laplace Transforms near Singular Points. Matematičeskie zametki, Tome 93 (2013) no. 6, pp. 920-931. http://geodesic.mathdoc.fr/item/MZM_2013_93_6_a9/