Geodesic
Asymptotic values of functions, analytic in planar domain
Problemy analiza, Tome 2 (2013) no. 1, pp. 38-42 Cet article a éte moissonné depuis la source Math-Net.Ru

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In [1] W. Gross constructed the example of an entire function of infinite order whose set of asymptotic values is equal to the extended complex plain. We obtain an analog of Gross' result for functions, analytic in planar domains of arbitrary connectivity with isolated boundary fragment.
Keywords: analytic function; asymptotic value; isolated boundary fragment. 
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E. G. Ganenkova; V. V. Starkov. Asymptotic values of functions, analytic in planar domain. Problemy analiza, Tome 2 (2013) no. 1, pp. 38-42. http://geodesic.mathdoc.fr/item/PA_2013_2_1_a2/

[1] Gross W., “Eine gauze Funktion für die jede Komplexe Zahl Konvergenzwert ist”, Math. Ann., 79 (1918), 201–208 | DOI | MR | Zbl

[2] Encyclopedia of Mathematics, [S. l.], v. 1 (A-B), Kluwer Academic Publishers, 1987

[3] Collingwood E. F., Lohwater A. J., The theory of cluster sets, Collingwood Lohwater Cambridge University Press, Cambridge, 1966 | MR

[4] Liczberski P., Starkov V. V., “On locally biholomorhic mappings from multi-connected onto simply connected domains”, Ann. Polon. Math., 85:2 (2005), 135–143 | DOI | MR | Zbl

[5] Goluzin G. M., Geometric Theory of Functions ofa Complex Variable, American Mathematical Scociety, Providence, R. I., 1969 | MR | Zbl

[6] Starkov V. V., “Locally biholomorphic mappings of multiconnected domains”, Sib. Math. J., 48:4 (2007), 733–739 | DOI | MR | Zbl