| Abstract: | In the paper a formal high-frequency solution of the problem of a point source of oscillations near a reflecting boundary is constructed. The boundary is geodesically concave which makes it possible to use methods developed in diffraction theory by V. A. Fock and J. B. Keller. On the basis of the formal solution of the problem of a point source of oscillations, it is possible to construct the asymptotics of the spectral functions of the Laplace-Beltrami operator.Translated fromZapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 89, pp. 14–53, 1979. |
