ИСТИНА

We consider problems of the following two types for a Helmholtz type equation: (i) the right-hand side is a function localized near some point of the domain: (ii) the equation is equipped with inhomogeneous boundary conditions, the boundary data being given by a function localized near some point of the boundary. The characteristic size of these sources is assumed to be of the order of the wave length. The high-frequency asymptotics of the solutions of these problems is constructed in terms of Maslov's canonical operator on pairs of Lagrangian manifolds under the assumption that there are no grazing rays involved.