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Some inequalities in the theory of functions

Published online by Cambridge University Press:  24 October 2008

W. K. Hayman
W. K. Hayman
Affiliation:
St John's CollegeCambridge
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Extract

In this paper we investigate the following problem.

We suppose given a sequence of complex values wn, defined for n = 0, 1, 2, …, and for n = ∞, and such that

while at least one wn differs from zero and ∞. We consider functions f(z), which are regular in | z | < 1, and take none of the sequence of values wn, and we investigate the effect of this restriction on the rate of growth of the function, as given by the maximum modulus

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 44 , Issue 2 , April 1948 , pp. 159 - 178
Copyright
Copyright © Cambridge Philosophical Society 1948

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References

REFERENCES

(1)Hayman, W. K.Some remarks on Schottky's theorem. Proc. Cambridge Phil. Soc. 43 (1947), 442–54.CrossRefGoogle Scholar
(2)Hayman, W. K.Some inequalities in the theory of functions. Proc. London Math. Soc. (in the Press).Google Scholar
(3)Littlewood, J. E.On inequalities in the theory of functions. Proc. London Math. Soc. (2), 23 (1924), 481–513.Google Scholar