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. 
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/
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