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Some weighted shifts associated with composition operators, fixed points, and iterates

Analyse Fonctionnelle

Lieu: 
Salle Kampé de Fériet M2
Orateur: 
George Exner
Affiliation: 
Bucknell University
Dates: 
Vendredi, 29 Septembre, 2017 - 14:00 - 15:00
Résumé: 
 
We consider composition operators $C_\varphi$ on $H^2$ induced by certain linear fractional transformations $\varphi$ mapping $\mathbb{D}$ into itself with the assumption that the Denjoy-Wolff point is $1$.  Certain restrictions of $C_\varphi^*$, arising from iterates under $\varphi$ of some point $z$ in the disk, are similar to weighted shifts.  The subnormality or hyponormality of the shift carries information about the (other) fixed point of $\varphi$ and the iteration point $z$ in pleasing geometrical ways (joint work with I. Chalendar).