On the Relation between the S-matrix and the Spectrum of the Interior Laplacian

摘要

The main results of this paper are:1)a proof that a necessary condition for 1 to be an eigenvalue of the S-matrix is realanalyticity of the boundary of the obstacle,2)a short proof that if 1 is an eigenvalue of the S-matrix, then k~2 is an eigenvalue ofthe Laplacian of the interior problem, and that in this case there exists a solution to theinterior Dirichlet problem for the Laplacian, which admits an analytic continuation to thewhole space R~3 as an entire function.