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.
