Punishing Factors for Finitely Connected Domains |
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Authors: | F G Avkhadiev K-J Wirths |
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Institution: | Kazan State University, Kazan, Russia Technische Universit?t Braunschweig, Germany
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Abstract: | Let Ω and Π be two finitely connected hyperbolic domains in the complex plane
and let R(z, Ω) denote the hyperbolic radius of Ω at z and R(w, Π) the hyperbolic radius of Π at w. We consider functions f that are analytic in Ω and such that all values f(z) lie in the domain Π. This set of analytic functions is denoted by A(Ω, Π). We prove among other things that the quantities
are finite for all
if and only if ∂Ω and ∂Π do not contain isolated points.
This work was supported by a grant of the Deutsche Forschungsgemeinschaft for F. G. Avkhadiev. |
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Keywords: | 2000 Mathematics Subject Classification: 30C80 30C55 |
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