Completeness of the Asymmetric Products of Solutions of a Second-Order Elliptic Equation and the Uniqueness of the Solution of an Inverse Problem for the Wave Equation

We establish the property of completeness in the space L-2 (D), where D is a domain in R-n, n >= 3, of the products of all possible regular solutions of the equation Delta u - K(2)u = 0, k is an element of R+boolean OR iR_, by the fundamental solutions of this equation with singularities on a straight line that does not meet (D) over bar. This result is used when establishing the uniqueness of the solution of a coefficient inverse problem of wave tomography in a nonoverdetermined statement.