This article is cited in 2 papers

Asymptotic Estimates of Functions Based on the Behavior of Their Laplace Transforms near Singular Points

O. A. Petruschov

M. V. Lomonosov Moscow State University

Abstract: 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.

Keywords: Laplace transform, nonmonotone real function, oscillation of a function, Riemann zeta-function, Dirichlet integral, Tauberian theorem, charge, measure.

UDC: 511.35+517.442

Received: 26.12.2011
Revised: 23.04.2012

DOI: 10.4213/mzm9302

 English version: Mathematical Notes, 2013, 93:6, 906–916

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