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Smooth majorants for functions of arbitrarily rapid growth

Published online by Cambridge University Press:  24 October 2008

J. P. Earl  and
W. K. Hayman
J. P. Earl
Affiliation:
Institute of Mathematics, Cornwallis Building, The University of Kent at Canterbury, Canterbury, Kent, CT2 7NF
W. K. Hayman
Affiliation:
Department of Mathematics, University of York, Heslington, York, YO1 5DD
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Extract

Valiron[3] showed that if f(z) is an entire function for which

where A(r) = log(sup{|f(z)|:|z| = r}), then there is a function x(r) = rρ(r) satisfying both

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 109 , Issue 3 , May 1991 , pp. 565 - 569
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

[1]Earl, J. P.. Note on the construction of proximate orders. J. London Math. Soc. 43 (1968), 695–698.Google Scholar
[2]Levin, B. Ya.. Distribution of zeros of entire functions. A.M.S. Translations of Mathematical Monographs, Vol. 5 (1964).CrossRefGoogle Scholar
[3]Valiron, G.. Lectures on the General Theory of Integral Functions (Privat, 1923).Google Scholar