Hadamard three-circle theorem
- Hadamard three-circle theorem
In complex analysis, a branch of mathematics, the Hadamard three-circle theorem is a result about the behavior of holomorphic functions.
Let be a holomorphic function on the annulus
:
Let be the maximum of on the circle Then, is a convex function of the logarithm Moreover, if is not of the form for some constants and , then is strictly convex as a function of
The conclusion of the theorem can be restated as
: for any three concentric circles of radii
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