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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $p$. 
@article{ISU_2014_14_3_a2,
     author = {E. G. Ganenkova},
     title = {Asymptotic {Values} of {Analytic} {Functions} {Connected} with a {Prime} {End} {of~a~Domain}},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {262--267},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a2/}
}
TY  - JOUR
AU  - E. G. Ganenkova
TI  - Asymptotic Values of Analytic Functions Connected with a Prime End of~a~Domain
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2014
SP  - 262
EP  - 267
VL  - 14
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a2/
LA  - ru
ID  - ISU_2014_14_3_a2
ER  - 
%0 Journal Article
%A E. G. Ganenkova
%T Asymptotic Values of Analytic Functions Connected with a Prime End of~a~Domain
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2014
%P 262-267
%V 14
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a2/
%G ru
%F ISU_2014_14_3_a2
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/