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) John McCarthy - Washington University, Titre Isometric extensions of bounded holomorphic functions Date 08/12/2022 Horaire 10:30 à 12:00 Diffusion Résume Let $V$ be an analytic subvariety of a domain $\Omega$ in $\C^n$. When does $V$ have the Isometric Extension Property (IEP), i.e. when does every bounded holomorphic function $f$ on $V$ has an  extension to a bounded holomorphic function on $\Omega$ with the same norm? If $V$ is a retract, i.e. if there exists  a holomorphic $r: \Omega \to V$ so that $r|_V = {\rm id}$,  then there is an obvious isometric extension, namely  $f \circ r$. If $\Omega$ is very nice, for example the ball, this condition is also necessary. We shall discuss why convexity assumptions lead to theorems that say only retracts have the IEP. If the convexity assumption is dropped, functional analysis can be used to show that every $V$ has the isometric extension property for some $\Omega$.  We shall discuss the proof of this theorem. This is joint work with Jim Agler and Lukasz Kosinski. Salle salle 13 - couloir 15-16 - 4ème étage Adresse Campus Pierre et Marie Curie