Displaying similar documents to “Equivalence of Boundary Eigenvalue Operator Fuctions and their Characteristic Matrix Functions.”

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

A. G. Ramm (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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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 real analyticity of the boundary of the obstacle, 2) a short proof 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.