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Mathematics of the USSR-Izvestiya, 1979, Volume 13, Issue 2, Pages 253–259
DOI: https://doi.org/10.1070/IM1979v013n02ABEH002042
(Mi im1886)
 

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

On the complete regularity of growth of the Borel transform of the analytic continuation of the associated function, which has a finite number of singular points

N. V. Govorov, N. M. Chernykh
References:
Abstract: The following theorem is proved. Let $A(z)$ be an entire function of exponential type, and let its Borel transform $a(z)$ satisfy the following conditions: 1) $a(z)$ can be analytically continued to a certain Riemann surface $R$ with finite number of branch points, and it has only finitely many singularities $z_k$ on $R$; 2) in any plane with cuts by parallel rays issuing from the $z_k$, a branch of $z_k$ satisfies
$$ \varlimsup_{z\to\infty}\frac{\ln|a(z)|}{|z|}\leq0. $$

Then $A(z)$ has completely regular growth. From this theorem it follows, in particular, that if $a(z)$ is an algebraic function or a single-valued function with a finite number of singularities, then $A(z)$ has completely regular growth.
Bibliography: 6 titles.
Received: 01.02.1977
Bibliographic databases:
UDC: 517.53
MSC: 30D15
Language: English
Original paper language: Russian
Citation: N. V. Govorov, N. M. Chernykh, “On the complete regularity of growth of the Borel transform of the analytic continuation of the associated function, which has a finite number of singular points”, Math. USSR-Izv., 13:2 (1979), 253–259
Citation in format AMSBIB
\Bibitem{GovChe78}
\by N.~V.~Govorov, N.~M.~Chernykh
\paper On the complete regularity of growth of the Borel transform of the analytic continuation of the associated function, which has a~finite number of singular points
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 2
\pages 253--259
\mathnet{http://mi.mathnet.ru//eng/im1886}
\crossref{https://doi.org/10.1070/IM1979v013n02ABEH002042}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=513909}
\zmath{https://zbmath.org/?q=an:0426.30022|0395.30019}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1979JD23800003}
Linking options:
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  • https://doi.org/10.1070/IM1979v013n02ABEH002042
  • https://www.mathnet.ru/eng/im/v42/i5/p965
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
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