Geodesic
Enforced Stability of a Simple Eigenvalue in the Continuous Spectrum of a Waveguide
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 3, pp. 37-53

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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.
Keywords: continuous spectrum, discrete spectrum, local perturbations of quantum waveguide.
Mots-clés : perturbation of eigenvalue 
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     author = {S. A. Nazarov},
     title = {Enforced {Stability} of a {Simple} {Eigenvalue} in the {Continuous} {Spectrum} of a {Waveguide}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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S. A. Nazarov. Enforced Stability of a Simple Eigenvalue in the Continuous Spectrum of a Waveguide. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 3, pp. 37-53. http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a3/