Geodesic
Asymptotic Values of Analytic Functions Connected with a Prime End of~a~Domain
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 3, pp. 262-267.

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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 $p$. 
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E. G. Ganenkova. Asymptotic Values of Analytic Functions Connected with a Prime End of~a~Domain. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 3, pp. 262-267. http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a2/

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