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On a problem of Bonar concerning Fatou points for annular functions

Published online by Cambridge University Press:  22 January 2016

Akio Osada
Akio Osada*
Affiliation:
Gifu College of Pharmacy
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The purpose of this paper is to study the distribution of Fatou points of annular functions introduced by Bagemihl and Erdös [1]. Recall that a function f(z), regular in the open unit disk D: | z | < 1, is referred to as an annular function if there exists a sequence {Jn} of closed Jordan curves, converging out to the unit circle C: | z | = 1, such that the minimum modulus of f(z) on Jn increases to infinity. If the Jn can be taken as circles concentric with C, f(z) will be called strongly annular.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 56 , January 1975 , pp. 163 - 170
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

[1] Bagemihl, F. and Erdös, P., A problem concerning the zeros of a certain kind of holomorphic function in the unit disk, J. Reine Angew. Math. 214/215 (1964), 340–344.CrossRefGoogle Scholar
[2] Barth, K. and Schneider, W., On a problem of Bagemihl and Erdös concerning the distribution of zeros of an annular function, J. Reine Angew. Math. 234 (1969), 179–183.Google Scholar
[3] Bonar, D. D., On annular functions, Springer, Berlin, 1971.Google Scholar
[4] Hoffman, K., Banach spaces of analytic functions, Prentice-Hall, Inc., 1962.Google Scholar
[5] Osada, A., On the distribution of zeros of a strongly annular function, Nagoya Math. J. (to appear).Google Scholar