Geodesic
On the Relation between the $S$-matrix and the Spectrum of the Interior Laplacian
A. G. Ramm1
1 Mathematics Department Kansas State University Manhattan, KS 66506-2602, U.S.A.
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) no. 2, pp. 181-188

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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 $k^2$ 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 $\mathbb R^3$ as an entire function.
DOI : 10.4064/ba57-2-11
Keywords: main results paper proof necessary condition eigenvalue s matrix real analyticity boundary obstacle short proof eigenvalue s matrix eigenvalue laplacian interior problem there exists solution interior dirichlet problem laplacian which admits analytic continuation whole space mathbb entire function

A. G. Ramm 1

1 Mathematics Department Kansas State University Manhattan, KS 66506-2602, U.S.A. 
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A. G. Ramm. On the Relation between the $S$-matrix and the Spectrum of the 
Interior Laplacian. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) no. 2, pp. 181-188. doi: 10.4064/ba57-2-11

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