turkmath.org

This talk is concerned with a class of holomorphic functions on the unit disc which have an extremely chaotic radial behaviour, namely the class of Abel universal functions. More specifically, for each such function f, the family {f_r : 0 < 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. After presenting connections with classical results and discussing the boundary behaviour of Abel universal functions, we will focus on their invariance under composition from the left and the right. As an application, we will see that the class of Abel universal functions has a rich algebraic structure. (Joint work with Stephane Charpentier and Konstantinos Maronikolakis.)