Séminaires : Séminaire d'Analyse Fonctionnelle

Equipe(s) : af,
Responsables :E. Abakoumov - A.Eskenazis - D. Cordero-Erausquin - M. Fathi - O. Guédon - B. Maurey
Email des responsables :
Salle : salle 13 - couloir 15-16 - 4ème étage
Adresse :Campus Pierre et Marie Curie
Le Jeudi à 10h30 -  IMJ-PRG - 4 place Jussieu - 75005 PARIS

Orateur(s) Konstantin Fedorovskiy - Moscow State Tech. Univ.,
Titre Badly approximable functions in L^p and analytic balayage of measures
Horaire10:30 à 14:55
RésumeThe first topic that we plan to consider is the concept of an analytic balayage of measures which was introduced by D. Khavinson in 1980-th. This concept turned out to be useful for studying properties of measures orthogonal to rational functions on compact sets in the complex plane. We present new formulae for analytic balayage of measures in the case when the support of a given measure lies inside some Carathéodory compact set, and the balayage is done onto the boundary of this compact set. It turnes out that this topic is closely related with properties of badly approximable functions in the space $L^1$ on the unit circle, that is such functions for which the best approximant in the Hardy space $H^1$ is the zero function. We will also discuss descriptions of badly approximable functions of class $L^p$ on the unit circle for all $p\geqslant1$. The talk is bases on a recent joint work of E. Abakumov and the author.
Sallesalle 13 - couloir 15-16 - 4ème étage
AdresseCampus Pierre et Marie Curie