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Eigenfunctions of the continuous spectrum of a waveguide with periodic boundary

Abstract

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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Literature cited

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    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.

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    O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968).

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    V. I. Derguzov, “The eigenfunctions of the continuous spectrum of a two-dimensional periodic optical waveguide,” J. Sov. Math.,35, No. 1 (1986).

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Additional information

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

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Keywords

  • Periodic Boundary
  • Continuous Spectrum