Abstract
The behavior of the poles zn(ɛ), n=1,2,... of the scattering matrix of the operatorl ɛu=−Δu(x), x ∈ Ω, ɛ(∂u/∂n)+σ(x)u|∂Ω=0 as ɛ→0 is considered. It is proved that |zn(ɛ)−zn|=0(ɛ(1/2)qn), where qn is the order of the pole of the scattering matrix for the operator ℝ0u=−δu, u/∂ω=0.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
P. D. Lax and R. S. Phillips, Scattering Theory, Academic Press (1967).
O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quaslilinear Elliptic Equations, Academic Press (1968).
T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag (1966).
S. V. Petras, “On the splitting of the series of resonances under unbounded growth of a barrier of ‘capture’ type,” in: Probl. Mat. Fiz., No. 8, 138–154 (1976).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 117, pp. 183–191, 1981.
Rights and permissions
About this article
Cite this article
Petras, S.V. Perturbation of the poles of the scattering matrix under variation of the boundary condition. J Math Sci 24, 380–386 (1984). https://doi.org/10.1007/BF01086998
Issue Date:
DOI: https://doi.org/10.1007/BF01086998