**Financial support through the following projects:**

UID/MAT/00297/2019

UID/MAT/00297/2013

PEst-OE/MAT/UI0297/2014

PEst-OE/MAT/UI0297/2011

Analisys Seminar

Speaker: Yuri Karlovich, Universidad Autónoma de Estado de Morelos, Cuernavaca, México

Date: 12/07/2017

Time: 2 pm

Place: Room 1.6, building. VII

Abstract:

A Fredholm symbol calculus is constructed for the C*-algebra generated on the space $L^2$ over the unit circle by the operators of multiplication by piecewise quasicontinuous functions, by the Cauchy singular integral operator and by the unitary shift operators related to a group $G$ of orientation-preserving diffeomorphists of the unit circle onto itself that have the same finite set of fixed points for all $g\in G\setminus\{e\}$. A Fredholm criterion for the operators in this C*-algebra is then established in

terms of their symbols. The talk is based on joint work with M.A. Bastos and C.A. Fernandes.