Abstract: | One presents a new two-scale expansion for the eigenfunctions of the whispering gallery type and the corresponding eigenvalues of the Laplace operator with the Dirichlet or Neumann condition in a plane domain.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 128, pp. 152–157, 1983. |