Hadamard's three-circle theorem

Hadamard's three-circle theorem

[′had·ə‚märdz ¦thrē ¦sər·kəl ′thir·əm]
(mathematics)
The theorem that if the complex function ƒ(z) is analytic in the ring a < |="">z |<>b, and if m (r) denotes the maximum value of |ƒ(z)| on the circle | z | = r with a <>r <>b, then log m (r) is a convex function of log r.