Literature Cited
N. N. Voitovich, B. Z. Katsenelenbaum, and A. N. Sivov, The Generalized Method of Natural Oscillations in Diffraction Theory [in Russian], Nauka, Moscow (1977).
M. S. Agranovich, Spectral Properties of Diffraction Problems [in Russian], Supplement to [1].
Z. N. Golubeva, “Some scalar diffraction problems, and related non-self-adjoint operators,” Radiotekh. Elektron.,21, No. 2, 219–227 (1976).
P. E. Berkhin, “A contribution to the diffraction problem for a thin screen,” Sib. Mat. Zh.,25, No. 1, 39–52 (1984).
S. L. Sobolev, Introduction to the Theory of Cubature Formulas [in Russian], Nauka, Moscow (1974).
H. Hönl, A. W. Maue, and K. Westpfahl, Theorie der Beugung, Handbuch der Physik, ed. S. Flügge, Band XXV/1, Springer-Verlag, Berlin (1961), pp. 218–573.
M. Sh. Birman and M. Z. Solomyak, “Asymptotics of the spectrum of differential equations,” in: Mathematical Analysis, Vol. 14 [in Russian], Itogi Nauki i Tekhniki, VINITI, Moscow (1977), pp. 5–58.
I. A. Solomeshch, “On the eigenvalues of some degenerate elliptic equations,” Mat. Sb.,54, No. 3, 295–310 (1961).
I. L. Vulis, “Spectral asymptotics of elliptic operators of arbitrary order with strong degeneracy on the boundary of the domain,” in: Problems of Mathematical Physics, Vol. 6 [in Russian], Leningrad State Univ. (1976), pp. 56–59.
Pham The Lai, “Operateurs elliptiques degeneres: comportement asymptotique du noyau de la resolvante et des valeurs propres,” C. R. Acad. Sci. Paris,280, No. 16, A1067-A1070 (1975).
Pham The Lai, “Comportement asymptotique du noyau de la resolvante et des valeurs propres d'une classe d'operateurs elliptique degeneres non necessariment autoadjoint,” J. Math. Pures Appl.,55, No. 4, 379–420 (1976).
M. Sable-Tougeron, “Comportement asymptotique des valeurs propres pour une classe d'operateurs elliptiques degeneres,” Tohoku Math. J.,30, No. 4, 581–605 (1978).
M. Guillemot-Teissier, “Proprietes spectrales des ceratin operateurs elliptique degeneres,” C. R. Acad. Sci. Baris,278, No. 3, A137-A140 (1974).
J. L. Lions and E. Magenes, Problèmes aux Limites non Homogènes et Applications, Dunod, Paris (1968).
V. B. Lidskii, “On the summability of series in the principal vectors of non-self-adjoint operatons,” Tr. Mosk. Mat. Obshch.,11, 3–35 (1962).
M. A. Shubin, Pseudodifferential Operators and Spectral Theory [in Russian], Nauka, Moscow (1978).
M. S. Agranovich, “Spectral properties of elliptic pseudodifferential operators on a closed curve,” Funkts. Anal. Prilozhen.,13, No. 4, 54–56 (1979).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 25, No. 2, pp. 55–66, March–April, 1984
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Berkhin, P.E. Spectral properties of the diffraction problem for a thin screen. Sib Math J 25, 211–221 (1984). https://doi.org/10.1007/BF00971459
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DOI: https://doi.org/10.1007/BF00971459