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Mat. Zametki, 2004, Volume 76, Issue 6, Pages 883–892 (Mi mz160)  

This article is cited in 3 scientific papers (total in 3 papers)

On the Zeros of Laplace Transforms

A. M. Sedletskii

M. V. Lomonosov Moscow State University

Abstract: Suppose that $f$ is a positive, nondecreasing, and integrable function in the interval $(0,1)$. Then, by Pólya's theorem, all the zeros of the Laplace transform
$$ F(z)=\int_0^1e^{zt}f(t) dt $$
lie in the left-hand half-plane $\operatorname{Re} z\le0$. In this paper, we assume that the additional condition of logarithmic convexity of $f$ in a left-hand neighborhood of the point $1$ is satisfied. We obtain the form of the left curvilinear half-plane and also, under the condition $f(+0)>0$, the form of the curvilinear strip containing all the zeros of $F(z)$.

DOI: https://doi.org/10.4213/mzm160

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English version:
Mathematical Notes, 2004, 76:6, 824–833

Bibliographic databases:

UDC: 517.5
Received: 21.10.2003

Citation: A. M. Sedletskii, “On the Zeros of Laplace Transforms”, Mat. Zametki, 76:6 (2004), 883–892; Math. Notes, 76:6 (2004), 824–833

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. M. Sedletskii, “Asymptotics of the Zeros of Degenerate Hypergeometric Functions”, Math. Notes, 82:2 (2007), 229–237  mathnet  crossref  crossref  mathscinet  isi  elib
    2. V. P. Zastavnyi, “On Zeros of Entire Functions of Special Form”, Math. Notes, 83:1 (2008), 23–30  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. A. Yu. Popov, A. M. Sedletskii, “Distribution of roots of Mittag-Leffler functions”, Journal of Mathematical Sciences, 190:2 (2013), 209–409  mathnet  crossref  mathscinet  zmath
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