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 Tr. Mat. Inst. Steklova, 2017, Volume 298, Pages 101–111 (Mi tm3813)

Holomorphic Mappings of a Strip into Itself with Bounded Distortion at Infinity

V. V. Goryainov

Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701 Russia

Abstract: A class of holomorphic self-mappings of a strip which is symmetric with respect to the real axis is studied. It is required that the mappings should boundedly deviate from the identity transformation on the real axis. Distortion theorems for this class of functions are obtained, and domains of univalence are found that arise for certain values of the parameter characterizing the deviation of the mappings from the identity transformation on the real axis.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00674-à Ministry of Education and Science of the Russian Federation ÍØ-9110.2016.1 This work was supported by the Russian Foundation for Basic Research (project no. 16-01-00674-a) and by a grant of the President of the Russian Federation (project no. NSh-9110.2016.1).

DOI: https://doi.org/10.1134/S0371968517030074

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English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 298, 94–103

Bibliographic databases:

UDC: 517.54

Citation: V. V. Goryainov, “Holomorphic Mappings of a Strip into Itself with Bounded Distortion at Infinity”, Complex analysis and its applications, Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar, Tr. Mat. Inst. Steklova, 298, MAIK Nauka/Interperiodica, Moscow, 2017, 101–111; Proc. Steklov Inst. Math., 298 (2017), 94–103

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3813
• https://doi.org/10.1134/S0371968517030074
• http://mi.mathnet.ru/eng/tm/v298/p101

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This publication is cited in the following articles:
1. V. V. Goryainov, “Loewner-Kufarev equation for a strip with an analogue of hydrodynamic normalization”, Lobachevskii J. Math., 39:6 (2018), 759–766
2. O. S. Kudryavtseva, A. P. Solodov, “Dvustoronnyaya otsenka oblastei odnolistnosti golomorfnykh otobrazhenii kruga v sebya s invariantnym diametrom”, Izv. vuzov. Matem., 2019, no. 7, 91–95
3. O. S. Kudryavtseva, A. P. Solodov, “Asimptoticheski tochnaya dvustoronnyaya otsenka oblastei odnolistnosti golomorfnykh otobrazhenii kruga v sebya s invariantnym diametrom”, Matem. sb., 211:11 (2020), 96–117
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