On a problem of Lohwater about the asymptotic behaviour in Nevanlinna’s class
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- by J. S. Hwang PDF
- Proc. Amer. Math. Soc. 81 (1981), 538-540 Request permission
Abstract:
Let $f(z)$ be meromorphic in $|z| < 1$ 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
- E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge University Press, Cambridge, 1966. MR 0231999
- A. J. Lohwater, On the Schwarz reflection principle, Michigan Math. J. 2 (1953/54), 151–156 (1955). MR 68624
Additional Information
- © Copyright 1981 American Mathematical Society
- 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