Hardy's theorem

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

• Maximum principle
• Hadamard three-circle theorem

References

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