Ramm, Alexander G.2011-03-072011-03-072009-03-01http://hdl.handle.net/2097/7979The main results of this paper are: 1) a proof that a necessary condition for 1 to be an eigenvalue of the S-matrix is real analyticity of the boundary of the obstacle, 2) a short proof of the conclusion stating that if 1 is an eigenvalue of the S-matrix, then k2 is an eigenvalue of the Laplacian of the interior problem, and that in this case there exists a solution to the interior Dirichlet problem for the Laplacian, which admits an analytic continuation to the whole space R3 as an entire function.This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).S-matrixWave scattering by obstaclesDiscrete spectrumScattering amplitudeArticle (author version)