2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58717We develop a scattering theory for perturbations of powers of the Laplacian on asymptotically Euclidean manifolds. The (absolute) scattering matrix is shown to be a Fourier integral operator associated to the geodesic flow at time πon the boundary. Furthermore, it is shown that on \Real^n the asymptotics of certain short-range perturbations of Δ^k can be recovered from the scattering matrix at a finite number of energies.To appear in the Canadian Journal of Mathematics; 26 pagesAnalysis of PDEsMathematical PhysicsSpectral Theory58J40; 58J20; 35P25text