Abstract
A dielectric periodic waveguide with almost arbitrary smooth boundary is studied. The existence of projecting and resolving operators is established. Bibliography: 9 titles.
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V. I. Derguzov and I. V. Denisova, “The characteristic spectrum of the reduced wave equation with periodic coefficients in the three-dimensional space”[in Russian], Probl. Mat. Anal. 21 (2000), 110–137; English transl.: J. Math. Sci., New York 105 (2001), no. 5, 2377–2397.
V. I. Derguzov and I. V. Denisova, “Invariant subspaces of three-dimensional periodic lightguides” [in Russian], Probl. Mat. Anal. 23 (2001), 3–13; English transl.: J. Math. Sci., New York 107 (2001), no. 3, 3807–3814.
I. V. Denisova, “Resolving operators for a three-dimensional periodic waveguide” [in Russian], Probl. Mat. Anal. 26 (2003), 67–86; English transl.: J. Math. Sci., New York 117 (2003), no. 3, 4109–4121.
V. I. Derguzov and I. V. Denisova, “Projecting and resolving operators for a three-dimensional waveguide” [in Russian], Probl. Mat. Anal. 30 (2005), 31–45; English transl.: J. Math. Sci., New York, 128 (2005), no. 5, 3195–3213.
V. I. Derguzov and I. V. Denisova, “Spreading waves in a three-dimensional dielectric periodic waveguide described by the generalized reduced wave equation” [in Russian], Probl. Mat. Anal. 29 (2004), 17–24; English transl.: J. Math. Sci., New York 124 (2004), no. 3
V. I. Derguzov and I. V. Denisova, “Projection operators of a three-dimensional periodic waveguide” [in Russian], Probl. Mat. Anal. 26 (2003), 87–139; English transl.: J. Math. Sci., New York 117 (2003), no. 3, 4122-4156.
O. A. Ladyzhenskaya and N. N. Uraltseva, Linear and Quasilinear Elliptic Equations [in Russian], Nauka, Moscow (1973); English transl. of the 1st ed.: Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968).
J.-L. Lions and E. Magenes, Nonhomogeneous Boundary-Value Problems and Applications, Berlin, Springer-Verlag (1972).
V. I. Derguzov and I. V. Denisova, “The problem about wave drop on the junction of two periodic dielectric waveguides” [in Russian] Vestnik St.Peterb. Gos. Univ, Ser. 1 (2006), no. 3, 27–33.
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Translated from Problemy Matematicheskogo Analiza, No. 35, 2007, pp. 47–57
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Derguzov, V.I. Projecting and resolving operators of a periodic waveguide. J Math Sci 144, 4581–4591 (2007). https://doi.org/10.1007/s10958-007-0296-x
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DOI: https://doi.org/10.1007/s10958-007-0296-x