Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Ganenkova E. G. Asymptotic Values of Analytic Functions Connected with a Prime End of a Domain. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 3, pp. 262-267. DOI: 10.18500/1816-9791-2014-14-3-262-267, EDN: SMSJTX

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
10.09.2014
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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.54
DOI: 
10.18500/1816-9791-2014-14-3-262-267
EDN: 
SMSJTX

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

Autors: 
Ganenkova Ekaterina Gennadevna, Petrozavodsk State University, 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, ∞∈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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Received: 
22.03.2014
Accepted: 
21.07.2014
Published: 
10.09.2014
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