Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-13T02:09:24.537Z Has data issue: false hasContentIssue false
  • English
  • Français

Tangential Boundary Properties of Arbitrary Functions in the Unit Disc

Published online by Cambridge University Press:  22 January 2016

Hidenobu Yoshida
Hidenobu Yoshida*
Affiliation:
Chiba University, Chiba
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

1. By the method of Dolzhenko’s paper, we studied relations between non-tangetial (angular) boundary behaviors and horocyclic boundary behaviors of arbitrary functions defined in the open unit disc of the complex plane in [8]. Vessey [5], [6] investigated the behavior of arbitrary functions on paths which are “more tangential” than horocycles. The purpose of the present paper is to prove the fact that is sharper than the results in Vessey [5], [6], and generalize the results in [8] to obtain the connection between behaviors on two “more tangential” angles.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 46 , March 1972 , pp. 111 - 120
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

[1] Bagemihl, F., Horocyclic boundary properties of meromorphic functions. Ann. Acad. Sci. Fenn., AI, 385, 1–18 (1966).Google Scholar
[2] Dragosh, S., Horocyclic cluster sets of functions defined in the unit disc. Nagoya Math. J. 35, 53–82 (1969).CrossRefGoogle Scholar
[3] Dolzhenko, E.P., Boundary properties of arbitrary functions. Izv. Akad. Nauk SSSR, 31, 3–14(1967). English translation: Math, of the USSR IZVESTIJA, 1, 1–12 (1967).Google Scholar
[4] Yanagihara, N., Angular cluster sets and oricyclic cluster sets. Proc. Japan Acad., 45, 423–428 (1969).Google Scholar
[5] Vessey, T.A., Tangential boundary behavior of arbitrary functions. Math. Z., 113, 113–118 (1970).CrossRefGoogle Scholar
[6] Vessey, T.A., On tangential principal cluster sets of normal meromorphic functions. Nagoya Math. J., 40, 133–137 (1970).CrossRefGoogle Scholar
[7] Collingwood, E.F. and Lohwater, A.J., The Theory of Cluster Sets. Camb. Univ. Press, Cambridge (1966).CrossRefGoogle Scholar
[8] Yoshida, H., Angular Cluster Sets and Horocyclic Angular Cluster Sets. Proc. Japan Acad., 47, 120–125 (1971).CrossRefGoogle Scholar