Abstract
It is shown in the paper that, under several orthogonality and normalization conditions and a proper choice of accessory parameters, a simple eigenvalue lying between thresholds of the continuous spectrum of the Dirichlet problem in a domain with a cylindrical outlet to infinity is not taken out from the spectrum by a small compact perturbation of the Helmholtz operator. The result is obtained by means of an asymptotic analysis of the augmented scattering matrix.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 47, No. 3, pp. 37–53, 2013
Original Russian Text Copyright © by S. A. Nazarov
This work was financially supported by RFBR grant no. 12-01-00348.
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Nazarov, S.A. Enforced stability of a simple eigenvalue in the continuous spectrum of a waveguide. Funct Anal Its Appl 47, 195–209 (2013). https://doi.org/10.1007/s10688-013-0026-8
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DOI: https://doi.org/10.1007/s10688-013-0026-8