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Proceedings of the American Mathematical Society

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On a problem of Lohwater about the asymptotic behaviour in Nevanlinna's class


Author: J. S. Hwang
Journal: Proc. Amer. Math. Soc. 81 (1981), 538-540
MSC: Primary 30D40
DOI: https://doi.org/10.1090/S0002-9939-1981-0601724-1
MathSciNet review: 601724
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Abstract: Let $ f(z)$ be meromorphic in $ \vert z\vert < 1$ and let the radial limits $ {\lim_{r \to 1}}f(r{e^{i\theta }})$ exist and have modulus 1 for almost all $ e^{i\theta} \in A = \{ e^{i\theta}: \theta_1 \leqslant \theta \leqslant \theta_2 \}$. If $ P$ is a singular point of $ f(z)$ on $ A$, then every value of modulus 1 which is not in the range of $ f(z)$ at $ P$ is an asymptotic value of $ f(z)$ at some point of each subarc of $ A$ containing the point $ P$. This answers in the affirmative sense a question of A. J. Lohwater.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0601724-1
Keywords: Asymptotic behaviour, Nevanlinna's class
Article copyright: © Copyright 1981 American Mathematical Society