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arXiv · 1410.6024

A characterization of Möbius transformations

Konstantin M. Dyakonov
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Abstract

We prove that the derivative $θ'$ of an inner function $θ$ is outer if and only if $θ$ is a Möbius transformation. An alternative characterization involving a reverse Schwarz--Pick type estimate is also given.

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Konstantin M. Dyakonov. 2014-10-22. A characterization of Möbius transformations. https://doi.org/10.1016/j.crma.2014.05.009

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