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On the coefficients and means of functions omitting values

Published online by Cambridge University Press:  24 October 2008

W. K. Hayman  and
A. Weitsman
W. K. Hayman
Affiliation:
Imperial College, London S. W. 7 and Purdue University, Lafayette, Indiana
A. Weitsman
Affiliation:
Imperial College, London S. W. 7 and Purdue University, Lafayette, Indiana
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Extract

Let

be regular in U = {|z| < 1}. Suppose that the values of f(z) all lie in a domain D in the w-plane. If certain geometrical restrictions are made on D we can deduce growth conditions on the maximum modulus

the means

and the coefficients αn. Good bounds for M(r, f) have been obtained under various conditions on D.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 1 , January 1975 , pp. 119 - 137
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

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