Functional Analysis and Applications Seminar 

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.