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Generalizations of Noshiro's Theorem and Their Applications

Published online by Cambridge University Press:  20 November 2018

Hidenobu Yoshida
Hidenobu Yoshida*
Affiliation:
Chiba University, Chiba-shi, Japan
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Meier [8, Hauptsatz] proved a remarkable theorem concerning the boundary behavior of functions meromorphic in the upper half plane; but his techniques are very complicated. So Noshiro [10, p. 72-73] proved an analogous (but somewhat weaker) result to Meier's by a simple method using the theorem of Gross and Iversen.

In this paper, we sharpen and generalize Noshiro's theorem in some directions by making use of the notion “porosity”, and we state some applications.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 3 , June 1973 , pp. 611 - 620
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Bagemihl, F., Curvilinear cluster sets of arbitrary functions, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 379–382.Google Scholar
2. Bagemihl, F., Meier points of holomorphic functions, Math. Ann. 155 (1964), 422–424.Google Scholar
3. Bagemihl, F., Horocyclic boundary properties of meromorphic functions, Ann. Acad. Sci. Fenn. Ser. A I 385 (1966), 1–18.Google Scholar
4. Bagemihl, F., Generalizations of two theorems of Meier concerning boundary behavior of meromorphic functions, Publ. Math. Debrecen U (1967), 53-55.Google Scholar
5. Collingwood, E. F. and Lohwater, A. J., The Theory of Cluster Sets (Cambridge University Press, Cambridge, 1966).Google Scholar
6. Dolzhenko, E. P., Boundary properties of arbitrary functions, Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 3-14. English translation: Math. USSR-Izv. 1 (1967), 1–12.Google Scholar
7. Dragosh, S., Horocyclic cluster sets of functions defined in the unit disc, Nagoya Math. J. 35 (1969), 53–82.Google Scholar
8. Meier, K., Über Mengen von Randwerten meromorpher Funktionen, Comment. Math. Helv. 30 (1955), 224–233.Google Scholar
9. Meier, K., Über die Randwerte der meromorphen Funktionen, Math. Ann. 142 (1961), 328–344.Google Scholar
10. Noshiro, K., Cluster sets (Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960).Google Scholar
11. Saks, S., Theory of the integral (Dover Publications, Inc., New York, 1964).Google Scholar
12. Vessey, T. A., Tangential boundary behavior of arbitrary functions, Math. Z. 113 (1970), 113–118.Google Scholar
13. Vessey, T. A., On tangential principal cluster sets of normal meromorphic functions, Nagoya Math. J. 40 (1970), 133–137.Google Scholar
14. Yanagihara, N., Angular cluster sets and oricyclic cluster sets, Proc. Japan Acad. 45 (1969), 423–428.Google Scholar
15. Yoshida, H., Tangential boundary properties of arbitrary functions in the unit disc, Nagoya Math. J. 46 (1972), 111–120.Google Scholar
16. Yoshida, H., Tangential boundary behaviors of meromorphic functions in the unit disc (to appear).Google Scholar