Hadamard's three-circle theorem

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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 ringa< |z|<b, and ifm(r) denotes the maximum value of |ƒ(z)| on the circle |z| =rwitha<r<b, then logm(r) is a convex function of logr.

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