Comptes Rendus
Complex Analysis
On boundary angular derivatives of an analytic self-map of the unit disk
[Un problème aux limites à dérivées non normales pour une application analytique du disque sur lui-même]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 5-6, pp. 227-230.

On se donne des nombres complexes s0,,sN, et on établit des conditions nécessaires et suffisantes d'existence d'une fonction analytique, définie sur le disque unité ouvert, bornée en module par un et admettant un développement asymptotique non tangentiel, en un point t0 du bord, du type f(z)=s0+s1(zt0)++sN(zt0)N+o((zt0)N). Ce critère peut être considéré commec l'analogue à la frontière du résultat classique de I. Schur.

Given complex numbers s0,,sN, we present necessary and sufficient conditions for the existence of a function f analytic and bounded by one in modulus on the open unit disk which admits the nontangential boundary asymptotic expansion f(z)=s0+s1(zt0)++sN(zt0)N+o((zt0)N) at a given point t0 on the unit circle. This criterion can be considered as a boundary analog of the classical result of I. Schur.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.01.018

Vladimir Bolotnikov 1

1 Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA
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Vladimir Bolotnikov. On boundary angular derivatives of an analytic self-map of the unit disk. Comptes Rendus. Mathématique, Volume 347 (2009) no. 5-6, pp. 227-230. doi : 10.1016/j.crma.2009.01.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.01.018/

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