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Труды Петрозаводского государственного университета. Математика, 2005, выпуск 12, страницы 51–70
(Mi pa62)
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Koebe domains for the class of typically real odd functions
L. Koczan, P. Zaprawa Lublin University of Technology, Department of Applied Mathematics, Lublin
Аннотация:
In this paper we discuss the generalized Koebe domains for the class $T ^{(2)}$ and the set $D\subset \Delta=\{z\in \mathbb{C}:|z|< 1\}$, i.e. the sets of the form $\cap_{f\in TM} f(D)$. The main idea we work with is the method of the envelope. We determine the Koebe domains for $H=\{z\in \Delta : |z^{2}+1|>2|z|\}$ and for special sets $\Omega_{\alpha}, \alpha \le \frac{4}{3}$. It appears that the set $\Omega_{\frac{4}{3}}$ is the largest subset of $\Delta$ for which one can compute the Koebe domain with the use of this method. It means that the set $K_{T^{(2)}}(\Omega_{\frac{4}{3}})\cup K_T (\Delta)$ is the largest subset of the still unknown set $K_{T^{(2)}}(\Delta)$ which we are able to derive.
Образец цитирования:
L. Koczan, P. Zaprawa, “Koebe domains for the class of typically real odd functions”, Труды ПГУ. Математика, 2005, no. 12, 51–70
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/pa62 https://www.mathnet.ru/rus/pa/y2005/i12/p51
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Страница аннотации: | 63 | PDF полного текста: | 48 |
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