Article Dans Une Revue Revista Matemática Iberoamericana Année : 2023

ABEL UNIVERSAL FUNCTIONS: BOUNDARY BEHAVIOUR AND TAYLOR POLYNOMIALS

Résumé

A holomorphic function f on the unit disc \mathbb{D} belongs to the class \mathcal{U}_{A} (\mathbb{D}) of Abel universal functions if the family \{f_{r}: 0\leq r<1\} of its dilates f_{r}(z):=f(rz) is dense in the space of continuous functions on K , for any proper compact subset K of the unit circle. It has been recently shown that \mathcal{U}_{A} (\mathbb{D}) is a dense G_{\delta} subset of the space of holomorphic functions on \mathbb{D} endowed with the topology of local uniform convergence. In this paper, we develop further the theory of universal radial approximation by investigating the boundary behaviour of functions in \mathcal{U}_{A} (\mathbb{D}) (local growth, existence of Picard points and asymptotic values) and the convergence properties of their Taylor polynomials outside \mathbb{D} .

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Dates et versions

hal-04939674 , version 1 (18-02-2025)
hal-04939674 , version 2 (30-04-2025)

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Stéphane Charpentier, Myrto Manolaki, Konstantinos Maronikolakis. ABEL UNIVERSAL FUNCTIONS: BOUNDARY BEHAVIOUR AND TAYLOR POLYNOMIALS. Revista Matemática Iberoamericana, In press, 41 (3), pp.867-890. ⟨10.4171/RMI/1514⟩. ⟨hal-04939674v1⟩
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