# Séminaires : Séminaire d'Analyse Fonctionnelle

 Equipe(s) : af, Responsables : E. Abakoumov - D. Cordero-Erausquin - G. Godefroy - O. Guédon - B. Maurey - G.Pisier Email des responsables : Salle : salle 13 - couloir 15-16 - 4ème étage Adresse : Campus Pierre et Marie Curie Description Le Jeudi à 10h30 -  IMJ-PRG - 4 place Jussieu - 75005 PARIS Lien vers les archives des années antérieures à 2015

 Orateur(s) Vassili Nestoridis - Univ. of Athens, Titre ANNULÉ - A new function algebra and Mergelyan type theorems Date 26/03/2020 Horaire 10:30 à 12:00 Diffusion Résume In arxiv:1901.01339, we gave a counterexample to a Mergelyan type statement for cartesian products stated by Gamelin and Garnett in an article published in TAMS fifty years ago, in 1969. In order to correct this false statement we introduced a natural algebra $A_D(K)$, smaller than the classical  algebra $A(K)$, where $K$ is a compact subset of $\Bbb C^d$. The introduction of $A_D(K)$ explains partially why approximation theory in several variables is not so developed and opens a new road of research. We believe that several new Mergelyan type theorems will be obtained. So far we have one such theorem for products and one for graphs. Applications to universality can be found in arxiv:1909.03521 and arxiv:1910.01759. Also, a parallel theory can be developed when replacing uniform convergence by uniform on $K$ convergence of all orders derivatives (in preparation). Salle salle 13 - couloir 15-16 - 4ème étage Adresse Campus Pierre et Marie Curie