Comptes Rendus
no. 7-8
Complex analysis/Harmonic analysis
A characterization of Möbius transformations

Presented by: Gilles Pisier

Konstantin M. Dyakonov1
1 ICREA and Universitat de Barcelona, Departament de Matemàtica Aplicada i Anàlisi, Gran Via 585, E-08007 Barcelona, Spain
Comptes Rendus. Mathématique, Volume 352 (2014) no. 7-8, pp. 593-595.

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.

Étant donnée une fonction intérieure θ, on démontre que sa dérivée θ′ est extérieure si et seulement si θ est une transformation de Möbius.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2014.05.009

Konstantin M. Dyakonov 1

1 ICREA and Universitat de Barcelona, Departament de Matemàtica Aplicada i Anàlisi, Gran Via 585, E-08007 Barcelona, Spain 
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Konstantin M. Dyakonov. A characterization of Möbius transformations. Comptes Rendus. Mathématique, Volume 352 (2014) no. 7-8, pp. 593-595. doi : 10.1016/j.crma.2014.05.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.05.009/

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[4] K.M. Dyakonov A reverse Schwarz–Pick inequality, Comput. Methods Funct. Theory, Volume 13 (2013), pp. 449-457

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