To the Problem of a Point Source in an Inhomogeneous Medium

This paper studies the asymptotic behavior with respect to the complex parameter of the fundamental solution for a second-order elliptic operator with smooth compact coefficients obtained by the V. P. Maslov canonical operator method using the results of V. V. Kucherenko. It is shown that the singular part of the asymptotics can be represented as a series in Hankel functions of the first kind. The asymptotics are constructed under the assumption that all trajectories of the corresponding Hamiltonian system go to infinity.