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On the boundary behavior of holomorphic functions in the unit disc

Published online by Cambridge University Press:  09 April 2009

Hidenobu Yoshida
Affiliation:
Department of MathematicsChiba University, Chiba City, Japan.
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Seidel (1959) established various boundary properties of holomorphic functions with spiral asymptotic paths. Especially, Theorem 4 which is the fundamental result of the paper; was generalized by Faust (1962), using essentially the same method that was employed by Seidel.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1976

References

Bagemihl, F. and Erdös, P. (1964), ‘A problem concerning the zeros of a certain kind of holomorphic function in the unit disc’, J. reine angew. Math. 214215 340–344.Google Scholar
Barth, K. and Schneider, W. J. (1969), ‘On a problem of Bagemihl and Erdös concerning the distribution of zeros of an annular function’, J. reine angew. Math. 234 179183.Google Scholar
Collingwood, E. F. and Lohwater, A. J. (1966), The theory of cluster sets (Camb. Univ. Press, 1966).CrossRefGoogle Scholar
Dolzhenko, E. P. (1967), ‘Boundary properties of arbitrary functions’, Izv. Akad. Nauk. SSSR 31 314.Google Scholar
English translation: Math. USSR-Izv. 1 112.Google Scholar
Dragosh, S. (1972), ‘The spherical derivative of meromorphic functions’, J. reine angew. Math. 252 5167.Google Scholar
Faust, Sister C. M. (1962), ‘On the boundary behavior of holomorphic functions in the unit disc’, Nagoya Math. J. 20 95103.Google Scholar
Saks, S. (1964), Theory of the integral (Dover Publications, Inc., 1964).Google Scholar
Seidel, W. (1959), ‘Holomorphic functions with spiral asymptotic paths’, Nagoya Math. J. 14 159171.CrossRefGoogle Scholar
Tsuji, M. (1959), Potential theory (Maruzen, Tokyo, 1959).Google Scholar