L.M.P.A
Laboratoire de Mathématiques Pures et Appliquées
Joseph Liouville

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

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

mars 2019 :