Abstract
We consider a three-dimensional periodic lightguide whose oscillations are described by the reduced wave equation. We study the spectrum of the waveguide operator in invariant subspaces. Bibliography: 6 titles.
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References
V. I. Derguzov and I. V. Denisova, “The characteristic spectrum of the reduced wave equation with periodic coefficients in the three-dimensional space,” Probl. Mat. Anal. [in Russian], 21, 110–137 (2000); English transl.: J. Math. Sci., 105, No. 5, 2377–2397 (2001).
V. I. Derguzov and I. V. Denisova, “Invariant subspaces of three-dimensional periodic lightguides,” Probl. Mat. Anal. [in Russian], 23, 3–13 (2001); English transl.: J. Math. Sci., 107, No. 3, 3807–3814 (2001).
B. G. Korenev, Introduction in the Theory of Bessel Functions [in Russian] Nauka, Moscow (1971).
S. G. Mikhlin, Linear Partial Differential Equations [in Russian], Nauka, Moscow (1977).
M. V. Fedoryuk, The Saddle-Point Method [in Russian], Nauka, Moscow (1977).
V. S. Vladimirov, Generalized Functions in Mathematical Physics [in Russian], Nauka, Moscow (1971).
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Derguzov, V.I., Denisova, I.V. The Spectrum of a Periodic Lightguide in Three-Dimensional Space. Journal of Mathematical Sciences 112, 3997–4014 (2002). https://doi.org/10.1023/A:1020049823827
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DOI: https://doi.org/10.1023/A:1020049823827