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Mat. Sb. (N.S.), 1975, Volume 96(138), Number 4, Pages 601–613 (Mi msb3413)  

This article is cited in 1 scientific paper (total in 2 paper)

On the growth of an entire function of exponential type on a sequence of points

A. F. Leont'ev


Abstract: We consider a function $F(\lambda)=\int_Ce^{\lambda t}d\sigma(t)$, where $C$ is an analytic arc whose tangent at each point makes an angle with the real axis of less than $\pi/4$ radians, and $\sigma(t)$ is a function of bounded variation on $C$ which is continuous from the left on $C$ and nonconstant in any neighborhood of the right end-point $b$. Suppose that $0<\lambda_k\uparrow\infty$, $\lambda_{k+1}-\lambda_k\geqslant h>0$ ($k\geqslant1$) and $\sum_1^\infty\lambda_k^{-1}=\infty$. We show that
$$ \varlimsup_{k\to\infty}\frac{\ln|F(\lambda_k)|}{\lambda_k}=\operatorname{Re}b. $$
When $C$ is a segment of the real axis, this result is well known.
Bibliography: 3 titles.

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English version:
Mathematics of the USSR-Sbornik, 1975, 25:4, 567–578

Bibliographic databases:

UDC: 517.535.4
MSC: 30A64
Received: 04.11.1974

Citation: A. F. Leont'ev, “On the growth of an entire function of exponential type on a sequence of points”, Mat. Sb. (N.S.), 96(138):4 (1975), 601–613; Math. USSR-Sb., 25:4 (1975), 567–578

Citation in format AMSBIB
\Bibitem{Leo75}
\by A.~F.~Leont'ev
\paper On~the growth of an entire function of exponential type on a~sequence of points
\jour Mat. Sb. (N.S.)
\yr 1975
\vol 96(138)
\issue 4
\pages 601--613
\mathnet{http://mi.mathnet.ru/msb3413}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=374425}
\zmath{https://zbmath.org/?q=an:0323.30025}
\transl
\jour Math. USSR-Sb.
\yr 1975
\vol 25
\issue 4
\pages 567--578
\crossref{https://doi.org/10.1070/SM1975v025n04ABEH002464}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. S. Vladimirov, S. M. Nikol'skii, Yu. N. Frolov, “Aleksei Fedorovich Leont'ev (on his sixtieth birthday)”, Russian Math. Surveys, 32:3 (1977), 131–144  mathnet  crossref  mathscinet  zmath
    2. Zeinstra R., “Zeros and Regular Growth of Laplace Transforms Along Curves”, J. Reine Angew. Math., 424 (1992), 1–15  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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