18/05/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building
Amarino Lebre, Instituto Superior Técnico, U.T. Lisboa
Factorization of singular integral operators with a
Carlemanbackward shift: the case of bounded measurable coefficients
This talk is based on a joint work with V. G. Kravchenko and J.
S. Rodríguez. We consider a generalization of the results of a
recent work by the authors concerning scalar singular integral
operators with a backward Carleman shift, allowing more general
coefficients, bounded measurable functions on the unit circle. The
main purpose is to obtain, for singular integral operators with a
backward shift and bounded measurable coefficients, an operator
factorization from which the Fredholm characteristics, like the
kernel and the cokernel, can be described. The main tool is the
factorization of matrix functions. In the course of the analysis
performed for that class of operators several useful
representations are obtained which permit, in particular, to
completely characterize the set of invertible operators in that
class, providing explicit examples of such operators.