On the Schwarz reflection principle

Author:
J. S. Hwang

Journal:
Trans. Amer. Math. Soc. **272** (1982), 711-719

MSC:
Primary 30D40

MathSciNet review:
662062

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Abstract: Recently, we have solved a long outstanding problem of A. J. Lohwater (1953) by showing that if is meromorphic in whose radial limits have modulus 1 for almost all points on an arc of , and if is a singular point of on , then every value of modulus 1 which is not in the range of at is an asymptotic value of at some point of each subarc of containing the point .

Lohwater proved this theorem for functions of bounded characteristic and he made a comment that his method is not, in general, applicable to functions of unbounded characteristic. In this paper, we shall present an alternative proof of the above theorem based on the very method of Lohwater.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1982-0662062-X

Keywords:
Asymptotic behaviour,
bounded characteristic,
reflection principle,
Seidel's class

Article copyright:
© Copyright 1982
American Mathematical Society