Functional Analysis and Applications Seminar 

03/11/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building
Sofia Naique, Instituto Superior Técnico, U.T. Lisboa

Polynomial almost periodic solutions for a class of Riemann-Hilbertproblems

We consider a class of Riemann-Hilbert problems with triangular symbols. Our investigation is devoted to the existence and calculation of a solution, in the form of an almost periodic polynomial. The Fourier spectrum of a solution of this kind is a subset of a particular additive group. A necessary and sufficient condition for the existence of a solution is obtained. Indeed, it is a simple condition on the Fourier spectrum of the matrix symbol. Explicit solutions are also determined, for different classes of Riemann-Hilbert problems, which are determined once again by the matrix symbol.