On the Completeness of Wave Operators under Loss of Local Compactness

We present a general criterion for the existence and completeness of the wave operators in obstacle (or potential) scattering which does not require local compactness near the boundary of the obstacle. The scope of our basic theorem is illustrated by new classes of examples, namely, exterior "Rooms and Passages"-domains, where completeness holds, and exterior "Jelly Roll"-domains, where it fails.