Properties of the far field operator for time harmonic acoustic waves

In this paper the eigenvalues of the far field operator according to the inverse scattering problem for time harmonic acoustic waves in the nonhomogeneous medium are characterized with an inequality. In addition to we prove the far field operator is one to one and its range is dense. In this paper we consider ∇ρ≠0∇ρ≠0, where ρ∈C1(IR3)ρ∈C1(IR3) is the density of the absorbing medium.