ch ao - d yn / 9 50 20 02 4 Fe b 19 95 Scattering Phases and Density of States for Exterior Domains

For a bounded open domain 2 R 2 with connected complement and piecewise smooth boundary, we consider the Dirichlet Laplacian on and the S-matrix on the complement c. Using the restriction A E of (E) 1 to the boundary of , we establish that A 1=2 E 0 1 is trace class when E 0 is negative and give bounds on the energy dependence of this difference. This allows for precise bounds on the total scattering phase, the definition of a-function, and a Krein spectral formula, which improve similar results found in the literature.