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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2014, Volume 14, Issue 3, Pages 262–267 (Mi isu508)  

Mathematics

Asymptotic Values of Analytic Functions Connected with a Prime End of a Domain

E. G. Ganenkova

Petrozavodsk State University, 33, Lenina ave., Petrozavodsk, 185910, Russia

Abstract: In 1954 M. Heins proved that for any analytic set $A$, containing the infinity, there exists an entire function with asymptotic set $A.$ In the article we prove the following analog of Heins's theorem: for a multi-connected planar domain $D$ with an isolated boundary fragment, an analytic set $A$, $\infty\in A$, and a prime end of $D$ with impression $p$ there exists an analytic in $D$ function $f$ such that $A$ is the set of asymptotic values of $f$ connected with $p$.

Key words: asymptotic set, prime end, analytic function, analytic set.

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Document Type: Article
UDC: 517.54

Citation: E. G. Ganenkova, “Asymptotic Values of Analytic Functions Connected with a Prime End of a Domain”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 14:3 (2014), 262–267

Citation in format AMSBIB
\Bibitem{Gan14}
\by E.~G.~Ganenkova
\paper Asymptotic Values of Analytic Functions Connected with a Prime End of~a~Domain
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2014
\vol 14
\issue 3
\pages 262--267
\mathnet{http://mi.mathnet.ru/isu508}


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  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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