| Abstract: | The ray method is used to obtain asymptotic equations for the complex eigenvalues of the Helmholtz equation. The problem of the transparent disk and oscillations of  transparent whispering gallery type are considered in detail.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 42, pp. 228–235, 1974.The author is grateful to V. M. Babich for a detailed discussion of the work and to A. L. Alimov, V. S. Buldyrev, and V. N. Krasil'nikov for useful discussions. |
