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

Orateur(s) John McCarthy - Washington University,
Titre Isometric extensions of bounded holomorphic functions
Date08/12/2022
Horaire10:30 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.

Sallesalle 13 - couloir 15-16 - 4ème étage
AdresseCampus Pierre et Marie Curie
© IMJ-PRG