One proves the existence of the eigenfunctions of the continuous spectrum of a two-dimensional waveguide with periodic boundary. One carries out a normalization of the eigenfunctions of the continuous spectrum relative to an indefinite inner product.
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D. Markuze (D. Marcuse), Optical Waveguides [Russian translation], Moscow (1974).
M. Adamo, Introduction to the Theory of Optical Waveguides [Russian translation], Moscow (1984).
V. I. Derguzov and I. B. Saikhanov, “The spectrum of a pellicular waveguide with a periodic boundary,” in: Studies in Stability and the Theory of Oscillations, Yaroslavl' (1981), pp. 18–39.
O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968).
V. I. Derguzov, “The eigenfunctions of the continuous spectrum of a two-dimensional periodic optical waveguide,” J. Sov. Math.,35, No. 1 (1986).
Translated from Problemy Matematicheskogo Analiza, No. 10, pp. 154–160, 1986.
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Malykhin, K.V. Eigenfunctions of the continuous spectrum of a waveguide with periodic boundary. J Math Sci 45, 1230–1235 (1989). https://doi.org/10.1007/BF01096155
- Periodic Boundary
- Continuous Spectrum