Seminário de Teoria de Operadores, Análise Complexa e Aplicações 

13/02/2014, 16:30 — 17:30 — Sala P3.10, Pavilhão de Matemática
Cristina Câmara, Instituto Superior Técnico

Riemann-Hilbert problems, Toeplitz operators and \(Q\)-classes

We generalize the notion of $Q$-classes $C_{Q_1,Q_2}$, which was introduced in the context of Wiener-Hopf factorization, by considering very general $2\times 2$ matrix functions $Q_1$, $Q_2$. This allows us to use a mainly algebraic approach to obtain several equivalent representations for each class, to study the intersections of $Q$-classes and to explore their close connection with certain non-linear scalar equations. The results are applied to various factorization problems and to the study of Toeplitz operators with symbol in a $Q$-class.