Abstract
Questions of the uniqueness of the solution to problems of scattering by a periodic lattice of obstacles are studied. By means of an analytic Fredholm theorem, it is proved that the set of scattering eigenfrequencies with values of the parameter of the Helmholtz equation for which there is nonuniqueness of the solution is discrete on a certain Riemann surface.
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 117, pp. 192–196, 1981.
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Sukhinin, S.V. Discreteness of the eigenfrequencies of scattering by a periodic lattice. J Math Sci 24, 386–389 (1984). https://doi.org/10.1007/BF01086999
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DOI: https://doi.org/10.1007/BF01086999