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On the Limit of the Modulus of a Bounded Regular Function
Published online by Cambridge University Press: 20 January 2009
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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.
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- Copyright © Edinburgh Mathematical Society 1964
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