Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 5, Pages 965–971 (Mi izv1886)  

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


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.

Full text: PDF file (571 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1979, 13:2, 253–259

Bibliographic databases:

UDC: 517.53
MSC: 30D15
Received: 01.02.1977

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”, Izv. Akad. Nauk SSSR Ser. Mat., 42:5 (1978), 965–971; 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 Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 5
\pages 965--971
\mathnet{http://mi.mathnet.ru/izv1886}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=513909}
\zmath{https://zbmath.org/?q=an:0426.30022|0395.30019}
\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 2
\pages 253--259
\crossref{https://doi.org/10.1070/IM1979v013n02ABEH002042}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JD23800003}


Linking options:
  • http://mi.mathnet.ru/eng/izv1886
  • http://mi.mathnet.ru/eng/izv/v42/i5/p965

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. N. V. Govorov, N. M. Chernykh, “Complete regularity of growth for some classes of entire functions of exponential type represented by Вorel integrals and power series”, Math. USSR-Izv., 27:3 (1986), 431–450  mathnet  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:224
    Full text:73
    References:36
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021