Hostname: page-component-5c6d5d7d68-wpx84 Total loading time: 0 Render date: 2024-08-15T13:23:34.545Z Has data issue: false hasContentIssue false
  • English
  • Français

An inequality for real positive functions

Published online by Cambridge University Press:  24 October 2008

W. K. Hayman
W. K. Hayman
Affiliation:
University CollegeExeter
Get access Rights & Permissions [Opens in a new window]

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

.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Borel, , É. Sur les zéros des fonctions entières. Acta math., Stockh., 20 (1897), 357–96.CrossRefGoogle Scholar
(2)Sierpinski, W.Un lemme métrique. Fundam. Math. 4 (1923), 301–3.CrossRefGoogle Scholar
(3)Titchmarsh, E. C.The theory of functions, 2nd ed. (Oxford, 1939).Google Scholar