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Hardy's theorem

In mathematics, Hardy's theorem is a result in complex analysis describing the behavior of a holomorphic function.

Let $f$ be a holomorphic function on the open ball of radius $R$ centered at zero and assume that $f$ is not a constant function. Then, if one defines

$I(r) = \frac{1}{2\pi} \int_0^{2\pi}\! \left| f(r e^{i\theta}) \right| \,d\theta,$

this function is strictly increasing logarithmically convex function.

References

John B. Conway. (1978) Functions of One Complex Variable I. Springer-Verlag, New York, New York.

Categories: Complex analysis

Last updated: 05-25-2005 19:37:02

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10-26-2009 08:16:03
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Hardy's theorem

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