Hardy's theorem

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

Let be a holomorphic function on the open ball centered at zero and radius in the complex plane, and assume that is not a constant function. If one defines

for then this function is strictly increasing and is a convex function of .

See also[edit]


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

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