Geodesic
Resonances and trapped modes in a quantum waveguide
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 9, pp. 1630-1638

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Properties of the eigenfunctions of the continuous spectrum of a self-adjoint differential second-order operator in a cylinder are investigated. It is proved that the eigenfunctions of the continuous spectrum are analytic with respect to the spectral parameter near the eigenvalues embedded in the continuous spectrum, and any eigenvalue embedded in the continuous spectrum is a removable singular point for the corresponding eigenfunctions. 
@article{ZVMMF_2005_45_9_a9,
     author = {A. A. Arsen'ev},
     title = {Resonances and trapped modes in a quantum waveguide},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1630--1638},
     publisher = {mathdoc},
     volume = {45},
     number = {9},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_9_a9/}
}
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A. A. Arsen'ev. Resonances and trapped modes in a quantum waveguide. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 9, pp. 1630-1638. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_9_a9/