Theorems in complex analysis | Inequalities

Hadamard three-circle theorem

In complex analysis, a branch of mathematics, theHadamard 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 (Wikipedia).

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Equation of a circle 3

Powered by https://www.numerise.com/ Equation of a circle 3

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Phragmén–Lindelöf principle | Convex function | Complex analysis | Hardy's theorem | Coefficient | Theorem | Logarithm | Logarithmically convex function | Maximum principle | Maxima and minima | Mathematics | Holomorphic function | Harmonic function | Borel–Carathéodory theorem | Hadamard three-lines theorem | Annulus (mathematics) | Edmund Landau | Jacques Hadamard | Circle