Geodesic
On descreteness of scattering eigenfrequences of periodic cascade
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 12, Tome 117 (1981), pp. 192-196

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The paper deals with the problem on the plane wave scattering on a periodic structure. A great number of the scattering eigenfre.quences, i. e. the parameter values of the Helmholtz equation, for which there is the solution non-uniqueness, has been proved to be discrete on a certain Riemann surface with the help of analytical Fredholm theorem. 
@article{ZNSL_1981_117_a13,
     author = {S. V. Sukhinin},
     title = {On descreteness of scattering eigenfrequences of periodic cascade},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {192--196},
     publisher = {mathdoc},
     volume = {117},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_117_a13/}
}
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S. V. Sukhinin. On descreteness of scattering eigenfrequences of periodic cascade. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 12, Tome 117 (1981), pp. 192-196. http://geodesic.mathdoc.fr/item/ZNSL_1981_117_a13/