no. 7-8
Complex analysis/Harmonic analysis
A characterization of Möbius transformations
[Une caractérisation des transformations de Möbius]

Présenté par : Gilles Pisier

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

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

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.05.009
Dyakonov, Konstantin M. 1

1 ICREA and Universitat de Barcelona, Departament de Matemàtica Aplicada i Anàlisi, Gran Via 585, E-08007 Barcelona, Spain 
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Dyakonov, Konstantin M. A characterization of Möbius transformations. Comptes Rendus. Mathématique, Tome 352 (2014) no. 7-8, pp. 593-595. doi : 10.1016/j.crma.2014.05.009. http://www.numdam.org/articles/10.1016/j.crma.2014.05.009/

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

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[6] Walsh, J.L. Note on the location of zeros of the derivative of a rational function whose zeros and poles are symmetric in a circle, Bull. Amer. Math. Soc., Volume 45 (1939), pp. 462-470

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