Seminário Análise Funcional e Aplicações 

11/11/2005, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Cristina Câmara, Instituto Superior Técnico, U.T. Lisboa

Riemann-Hilbert problems, factorization of functions and structure of the factors

Let $G$ be a $2\times 2$ matrix function of Daniele-Khrapkov type. An equivalence between linear Riemann-Hilbert problems with coefficient $G$ and a class of scalar boundary value problems relative to a contour in a Riemann surface $\Sigma$ is established. By studying the solutions of these problems, it can be shown that the solution of the former Riemann-Hilbert problems must satisfy certain relations. In particular, if $G$ admits a canonical bounded factorization, it follows that the factors must have a certain structure.