Laboratoire de Mathématiques Pures et Appliquées
Joseph Liouville

Groupe de travail de Probabilités, statistiques, théorie ergodique du 28 février 2019

Nikolitsa Chatzigiannakidou (ULCO)

In this talk we are interested in universality phenomena. To be more explicit, if we consider a sequence of operators $T_n : X\rightarrow Y$, ($n\in\mathbb{N}$), where $X$ and $Y$ are metric spaces, an element $x\in X$ is called universal if every element of $Y$ can be approximated by a subsequence of $(T_nx)_n$. Let $X=H(\Omega)$ be the space of all holomorphic functions in a simply connected domain $\Omega\subset \mathbb{C}$ (with the topology of uniform convergence on compacta). We will focus on classes of holomorphic functions $f$, such that the pairs $(S_n(f), S_{\lambda_n}(f))_n$ perform approximations (where $S_n(f)$ is the sequence of partial sums of the Taylor expansion of $f$, around a point $\zeta\in \Omega$ and $(\lambda_n)_n$ is a strictly increasing sequence of positive integers). These functions, called doubly universal Taylor series, are universal elements for a suitable sequence of operators. We will investigate this class of functions, generalizing a result of G. Costakis and N. Tsirivas. They introduced in 2014 the concept of double universality for Taylor series, inspired by the notion of disjointness in dynamical systems.

Informations : 15:30 - 16:30 Salle C115