Abstract
Integral equations of a three-dimensional periodic lightguide are studied for arbitrary values of the frequency parameter. The solution to the homogeneous integral equation vanishes for those values of the spectral parameter that are different from some isolated points. Bibliography: 5 titles.
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References
I. B. Saikhanov, “The spectrum of a dielectric waveguide with periodic boundary,”Vestn. Leningr. Univ., Mat. Mekh. Astron., Issue 4, 103–104 (1982).
V. I. Derguzov and I. B. Saikhanov, “Point spectrum of a filament waveguide near singular points of a spectral parameter,”Vestn. Leningr. Univ., Mat. Mekh. Astron., Issue 4, 9–15 (1982).
V. I. Derguzov, “Normalization of eigenfunctions of the continuous spectrum of a three-dimensional periodic lightguide,”J. Math. Sci.,92, No. 6, 4273–4285 (1997).
V. I. Derguzov, “Orthogonalization of eigenfunctions of a three-dimensional lightguide,”Vestn. St. Petersburg. Univ., Ser. I, Mat. Mekh. Astron., Issue 1, 6–9 (1998).
B. G. Korenev,Introduction to the Theory of Bessel Functions [in Russian], Nauka, Moscow (1971).
Additional information
Translated fromProblemy Matematicheskogo Analiza, No. 19, 1999, pp. 89–100.
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Derguzov, V.I. The solvability of integral lightguide equations. J Math Sci 101, 2930–2937 (2000). https://doi.org/10.1007/BF02672178
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DOI: https://doi.org/10.1007/BF02672178