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Probl. Anal. Issues Anal., 2015, Volume 4(22), Issue 2, Pages 23–31 (Mi pa193)  

On asymptotic values of functions in a polydisk domain and Bagemihl's theorem

E. G. Ganenkova

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

Abstract: Asymptotic sets of functions in a polydisk domain of arbitrary connectivity are studied. We construct an example of such function, having preassigned asymptotic set. This result generalizes well-known examples, obtained by M. Heins and W. Gross for entire functions. Moreover, it is found out that not all results on asymptotic sets of functions in $\mathbb{C}$ can be extended to functions in $\mathbb{C}^n$. In particular, this fact is connected with the failure of Bagemihl's theorem on ambiguous points for functions in $\mathbb{R}^n,$ $n\geq 3$.

Keywords: asymptotic value, analytic set, ambiguous point

DOI: https://doi.org/10.15393/j3.art.2015.2951

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Document Type: Article
UDC: 517.57
MSC: 32A40, 26B99
Received: 10.12.2015
Language: English

Citation: E. G. Ganenkova, “On asymptotic values of functions in a polydisk domain and Bagemihl's theorem”, Probl. Anal. Issues Anal., 4(22):2 (2015), 23–31

Citation in format AMSBIB
\Bibitem{Gan15}
\by E.~G.~Ganenkova
\paper On asymptotic values of functions in a polydisk domain and Bagemihl's theorem
\jour Probl. Anal. Issues Anal.
\yr 2015
\vol 4(22)
\issue 2
\pages 23--31
\mathnet{http://mi.mathnet.ru/pa193}
\crossref{https://doi.org/10.15393/j3.art.2015.2951}
\elib{http://elibrary.ru/item.asp?id=26694849}


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