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An inequality for real positive functions

Published online by Cambridge University Press:  24 October 2008

W. K. Hayman
W. K. Hayman
Affiliation:
University CollegeExeter
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Extract

In the theory of functions of a complex variable a positive quantity g(r), denned in terms of a circle |z| = r, can often be estimated by means of another similar quantity f(R) denned in terms of a circle |z| = R with R > r. Inequalities of the form

arise in this connexion. Putting R = r + h we have for every h > 0

.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 48 , Issue 1 , January 1952 , pp. 93 - 105
Copyright
Copyright © Cambridge Philosophical Society 1952

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References

REFERENCES

(1)Borel, , É. Sur les zéros des fonctions entières. Acta math., Stockh., 20 (1897), 357–96.CrossRefGoogle Scholar
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(3)Titchmarsh, E. C.The theory of functions, 2nd ed. (Oxford, 1939).Google Scholar