  This paper concerns hyperbolic systems of two linear first-order PDEs in one
space dimension with periodicity conditions in time and reflection boundary
conditions in space. The coefficients of the PDEs are supposed to be time
independent, but allowed to be discontinuous with respect to the space
variable. We construct two scales of Banach spaces (for the solutions and for
the right hand sides of the equations, respectively) such that the problem can
be modeled by means of Fredholm operators of index zero between corresponding
spaces of the two scales.
