# 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).