On the relation between the S-matrix and the spectrum of the interior Laplacian

• Autorzy: Ramm, A. G.
• 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.

Słowa kluczowe

EN

wave scattering by obstacles; S-matrix; scattering amplitude

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: Vol. 57, no 2
• Strony: 181-188
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Ramm, A. G.

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

Bibliografia

• [1] B. Dietz, J.-P. Eckmann, C.-A. Fillet and U. Smilansky, Inside-outside duality for planar billiards: A numerical study, Phys. Rev. E 51 (1995), 4222-4231.
• [2] E. Doron and U. Smilansky, Semiclassical quantization of chaotic billiards: a scattering approach, Nonlinearity 5 (1992), 1055-1084.
• [3] J.-P. Eckmann and C.-A. Pillet, Spectral duality for planar billiards, Comm. Math. Phys. 170 (1995), 283-313.
• [4] B. A. Fuks, Theory of Analytic Functions of Several Variables, Amer. Math. Soc., Providence, RI, 1963.
• [5] A. G. Ramm, Scattering by Obstacles, Reidel, Dordrecht, 1986.