Comptes Rendus
no. 7
Complex analysis/Functional analysis
On the boundary behaviour of derivatives of functions in the disc algebra
[Sur le comportement au bord de dérivées de fonctions de l'algèbre du disque]

Présenté par : the Editorial Board

Stéphane Charpentier1 ; Vassili Nestoridis2
1 Institut de mathématiques de Marseille, UMR 7353, Aix-Marseille Université, Technopôle Château-Gombert, 39, rue Frédéric-Joliot-Curie, 13453 Marseille cedex 13, France
2 Department of Mathematics, National and Kapodistrian University of Athens, 15784 Athens, Greece
Comptes Rendus. Mathématique, Volume 356 (2018) no. 7, pp. 732-736.

On présente une construction simple et explicite d'une fonction de l'algèbre du disque dont les dérivés possèdent des propriétés d'universalité disjointe au bord. L'ensemble des fonctions ayant une telle propriété est topologiquement générique et contient un sous-espace dense et un sous-espace fermé de dimension infinie.

We provide with a simple and explicit construction of a function in the disc algebra, whose derivatives enjoy a disjoint universal property near the boundary. The set of functions with such property is topologically generic, densely lineable, and spaceable.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.05.015
Stéphane Charpentier 1 ; Vassili Nestoridis 2

1 Institut de mathématiques de Marseille, UMR 7353, Aix-Marseille Université, Technopôle Château-Gombert, 39, rue Frédéric-Joliot-Curie, 13453 Marseille cedex 13, France
2 Department of Mathematics, National and Kapodistrian University of Athens, 15784 Athens, Greece 
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Stéphane Charpentier; Vassili Nestoridis. On the boundary behaviour of derivatives of functions in the disc algebra. Comptes Rendus. Mathématique, Volume 356 (2018) no. 7, pp. 732-736. doi : 10.1016/j.crma.2018.05.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.05.015/

[1] R.M. Aron; L. Bernal-González; D.M. Pellegrino; J.B. Seoane Sepúlveda Lineability: The Search for Linearity in Mathematics, Monographs and Research Notes in Mathematics, CRC Press, Boca Raton, FL, USA, 2016

[2] F. Bagemihl; W. Seidel Some boundary properties of analytic functions, Math. Z., Volume 61 (1954) no. 1, pp. 186-199

[3] F. Bayart Universal radial limits of holomorphic functions, Glasg. Math. J., Volume 47 (2005) no. 2, pp. 261-267

[4] F. Bayart; K.-G. Grosse-Erdmann; V. Nestoridis; C. Papadimitropoulos Abstract theory of universal series and applications, Proc. Lond. Math. Soc., Volume 96 (2008), pp. 417-463

[5] L. Bernal-González Disjoint hypercyclic operators, Stud. Math., Volume 182 (2007) no. 2, pp. 113-131

[6] L. Bernal-González; D. Pellegrino; J.B. Seoane-Sepúlveda Linear subsets of nonlinear sets in topological vector spaces, Bull. Amer. Math. Soc., Volume 51 (2014) no. 1, pp. 71-130

[7] J. Bès; A. Peris Disjointness in hypercyclicity, J. Math. Anal. Appl., Volume 336 (2007) no. 1, pp. 297-315

[8] Y. Dupain Extension à la dimension n d'un théorème de Ortel et Schneider, Math. Z., Volume 206 (1991) no. 1, pp. 71-80

[9] S.J. Gardiner Universal Taylor series, conformal mappings and boundary behaviour, Ann. Inst. Fourier (Grenoble), Volume 64 (2014) no. 1, pp. 327-339

[10] T. Hatziafratis; K. Kioulafa; V. Nestoridis On Bergman type spaces of holomorphic functions and the density, in these spaces, of certain classes of singular functions, Complex Var. Elliptic Equ. (2017)

[11] J.-P. Kahane; Y. Katznelson Sur le comportement radial des fonctions analytiques, C. R. Acad. Sci. Paris, Ser. A, Volume 272 (1971), pp. 718-719

[12] S. Krantz Smoothness to the boundary of biholomorphic mappings: an overview (K. Jarosz, ed.), Contemporary Mathematics, vol. 645, American Mathematical Society, Providence, Rhode Island, 2015, pp. 179-190 | DOI

[13] Q. Menet Hypercyclic subspaces and weighted shifts, Adv. Math., Volume 255 (2014), pp. 305-337

[14] V. Nestoridis Universal Taylor series, Ann. Inst. Fourier (Grenoble), Volume 46 (1996), pp. 1293-1306

[15] V. Nestoridis Domains of holomorphy, Ann. Math. Qué., Volume 42 (2018) no. 1, pp. 101-105

[16] P. Painlevé Sur les lignes singulières des fonctions analytiques, 1887 (PhD thesis)

[17] M. Siskaki Boundedness of derivatives and anti-derivatives of holomorphic functions as a rare phenomenon, J. Math. Anal. Appl., Volume 462 (2018) no. 2, pp. 1073-1086

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