On boundary angular derivatives of an analytic self-map of the unit disk
نویسنده
چکیده
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) + o((z − t0) ) 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. To cite this article: V. Bolotnikov, C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved. Résumé Un problème aux limites à dérivées non normales pour une application analytique du disque sur lui-même. 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) + o((z − t0) ). Ce critère peut être considéré commec l’analogue à la frontière du résultat classique de I. Schur. Pour citer cet article : V. Bolotnikov, C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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