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. 
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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/

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