Spectral Duality for Planar Billiards

J. -P. Eckmann, C. -A. Pillet

For a bounded open domain $\Omega$ with connected complement in ${\mathbf{R}}^2$ and piecewise smooth boundary, we consider the Dirichlet Laplacian $-{\Delta }_{\Omega }$ on $\Omega$ and the S-matrix on the comp…