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

• Autorzy: A. G. Ramm
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 78A45: Diffraction, scattering
• 35J25: Boundary value problems for second-order elliptic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: 57
• Numer: 2
• Strony: 181-188

Daty

wydano

2009

Twórcy

autor

A. G. Ramm

• Mathematics Department, Kansas State University, Manhattan, KS 66506-2602, U.S.A.

Identyfikatory

DOI

10.4064/ba57-2-11