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The iteration of entire functions of small growth

Published online by Cambridge University Press:  24 October 2008

Gwyneth M. Stallard
Gwyneth M. Stallard
Affiliation:
Department of Mathematics, Imperial College of Science, Technology and Medicine, LondonSW7 2AZ
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Abstract

We show that if a transcendental entire function has order zero and sufficiently small growth or has order ρ < ½ and regular growth then its set of normality has no unbounded components.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 1 , July 1993 , pp. 43 - 55
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

REFERENCES

[1]Baker, I. N.. Zusammensetzungen ganzer Funktionen. Math. Z. 69 (1958), 121–163.CrossRefGoogle Scholar
[2]Baker, I. N.. The iteration of polynomials and transcendental entire functions. J. Austral. Math. Soc. 30 (1981), 483–495.CrossRefGoogle Scholar
[3]Cartwright, M. L.. Integral Functions (Cambridge University Press, 1965).Google Scholar
[4]Fatou, P.. Sur les equations fonctionelles. Bull. Soc. Math. France 47 (1919), 167–271Google Scholar
[4]Fatou, P.. Sur les equations fonctionelles. Bull. Soc. Math. France 48 (1920), 33–94, 208–314.CrossRefGoogle Scholar
[5]Fatou, P.. Sur l'itération des fonctions transcendantes entières. Acta. Math. 47 (1926), 337–370.CrossRefGoogle Scholar
[6]Titchmarsh, E. C.. The Theory of Functions (Oxford University Press, 1939).Google Scholar