A class of ordinary differential operators with jump boundary conditions

In this paper, we study a class of differential operators which are second order, matrix coefficient Schrödinger operators with infinitely many jump conditions. Our operators are more general than those occurring in dispersive billiards, in other words, dispersive geodesic flow on Riemannian manifold with boundary, but include these as a special case. In this case, the jump conditions correspond to the reflections. A derivation of the jump conditions for dispersive billiards on m dimensional Riemannian manifold with boundary is included.