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.
