Complex Analysis
On boundary angular derivatives of an analytic self-map of the unit disk

Presented by: Gilles Pisier

Bolotnikov, Vladimir1
1 Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA
Comptes Rendus. Mathématique, Volume 347 (2009) no. 5-6, pp. 227-230.

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(z−t0)+⋯+sN(z−t0)N+o((z−t0)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.

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(z−t0)+⋯+sN(z−t0)N+o((z−t0)N). Ce critère peut être considéré commec l'analogue à la frontière du résultat classique de I. Schur.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.01.018
Bolotnikov, Vladimir 1

1 Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA 
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Bolotnikov, Vladimir. 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. http://www.numdam.org/articles/10.1016/j.crma.2009.01.018/

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