Functional Analysis and Applications Seminar 

04/05/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building
Juan Carlos Sanchez Rodríguez, Universidade do Algarve, Faro

Factorization of singular integral operators with a Carleman backward shift: the case of continuous coefficients

It is well known that when dealing with (pure) singular integral operators on the unit circle with coefficients belonging to a decomposing algebra of continuous functions, a factorization of the symbol induces a factorization of the original operator, which is a representation of the operator as a product of three singular integral operators where the outer operators in that representation are invertible. In our seminar we will show a similar operator factorization for the case of singular integral operators with a backward shift. We also show that the factorization of the considered operators is related to a (special) factorization in a algebra of block diagonal matrix functions and that such operator factorization is also possible for other classes of singular integral operators, namely those including either a conjugation operator or a composition of a conjugation with a forward shift operator.