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On the Limit of the Modulus of a Bounded Regular Function

Published online by Cambridge University Press:  20 January 2009

N. A. Bowen
N. A. Bowen
Affiliation:
The UniversityLeicester
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M. L. Cartwright has given ((2), 180–181) the following theorem, together with a neat proof of it.

Theorem C.Suppose that f(z) is regular and

in the half-strip S

of the complex plane.

Suppose also that for some constant α in α<a<β

as y→∞. Then for every δ>0.

uniformly asy→∞ for α+δ≦x≦β–δ.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 14 , Issue 1 , June 1964 , pp. 21 - 24
Copyright
Copyright © Edinburgh Mathematical Society 1964

References

REFERENCE

(1) Boas, R. P., Entire Functions (New York, 1954).Google Scholar
(2) Cartwright, M. L., Journal London Math. Soc., 37 (1962), 179–184.CrossRefGoogle Scholar
(3) Hardy, Ngham and Pólya, , Proc. London Math. Soc. (2), 27 (1928), 401–409.CrossRefGoogle Scholar
(4) Titchmarsh, E. C., Theory of Functions (Oxford, 1939).Google Scholar