Titre :

On doubly universal functions

Auteur(s) :

Mouze, A [Auteur]
Centrale Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Discipline(s) HAL :

Mathématiques [math]/Analyse classique [math.CA]
Mathématiques [math]/Variables complexes [math.CV]
Mathématiques [math]/Analyse fonctionnelle [math.FA]

Résumé en anglais : [en]

Let $(\lambda_n)$ be a strictly increasing sequence of positive integers. Inspired by the notions of topological multiple recurrence and disjointness in dynamical systems, Costakis and Tsirivas have recently established ...
Lire la suite >Let $(\lambda_n)$ be a strictly increasing sequence of positive integers. Inspired by the notions of topological multiple recurrence and disjointness in dynamical systems, Costakis and Tsirivas have recently established that there exist power series $\sum_{k\geq 0}a_kz^k$ with radius of convergence 1 such that the pairs of partial sums $\{(\sum_{k=0}^na_kz^k,\sum_{k=0}^{\lambda_n}a_kz^k): n=1,2,\dots\}$ approximate all pairs of polynomials uniformly on compact subsets $K\subset\{z\in\mathbb{C} :\vert z\vert>1\},$ with connected complement, if and only if $\limsup_{n}\frac{\lambda_n}{n}=+\infty.$ In the present paper, we give a new proof of this statement avoiding the use of advanced tools of potential theory. It allows to obtain the algebraic genericity of the set of such power series and to study the case of doubly universal infinitely differentiable functions. Further we show that the Ces\`aro means of partial sums of power series with radius of convergence 1 cannot be frequently universal.Lire moins >

Langue :

Anglais

Commentaire :

submitted to a journal on september 27th, 2015

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T17:49:17Z