Functional Analysis and Applications Seminar 

08/02/2008, 15:00 — 16:00 — Room P3.10, Mathematics Building
Cristina Câmara, Instituto Superior Técnico, UT Lisboa

The classes $C(Q,R)$, matrix factorization and Riemann-Hilbert problems in a Riemann surface

A family of classes $C(Q,R)$ which include all $2\times 2$ factorable matrices with Hölder continuous entries in the unit circle is defined. It is shown that an appropriate characterization of such classes enables one to associate, in a unique way, an algebraic curve to each class $C(Q,R)$ and to show the equivalence of a Riemann-Hilbert problem with matrix coefficient in that class to a scalar Riemann-Hilbert problem in a Riemann surface. This is joint work with A. F. dos Santos and Pedro F. dos Santos.