Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
MathSciNet review: 601724
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30D40

Retrieve articles in all journals with MSC: 30D40

Additional Information

Keywords: Asymptotic behaviour, Nevanlinna's class
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society