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Matematicheskie Zametki, 2013, Volume 93, Issue 6, Pages 920–931
DOI: https://doi.org/10.4213/mzm9302 (Mi mzm9302) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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

O. A. Petruschov

M. V. Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm9302
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.
Received: 26.12.2011
Revised: 23.04.2012
English version:
Mathematical Notes, 2013, Volume 93, Issue 6, Pages 906–916
DOI: https://doi.org/10.1134/S0001434613050283
Bibliographic databases:
Document Type: Article
UDC: 511.35+517.442
Language: Russian
Citation: O. A. Petruschov, “Asymptotic Estimates of Functions Based on the Behavior of Their Laplace Transforms near Singular Points”, Mat. Zametki, 93:6 (2013), 920–931; Math. Notes, 93:6 (2013), 906–916
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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