TY - GEN A1 - Kmit, Irina A1 - Recke, Lutz T1 - Fredholm Alternative for Periodic-Dirichlet Problems for Linear Hyperbolic Systems N2 - 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. The main tools of the proofs are separation of variables, integral representation of the solutions of the corresponding boundary value problems of the ODE systems and an abstract criterion for Fredholmness which seems to be new. KW - no small denominators KW - dissipative hyperbolic system Y1 - 2006 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/354 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-3542 ER -