Abstract
ABSTRACTWe consider the scattering theory for a pair of operators H0 and H = H0 + V on L2(M, m), where M is a Riemannian manifold, H0 is a multiplication operator on M, and V is a pseudodifferential operator of order − μ, μ > 1. We show that a time-dependent scattering theory can be constructed, and the scattering matrix is a pseudodifferential operator on each energy surface. Moreover, the principal symbol of the scattering matrix is given by a Born approximation type function. The main motivation of the study comes from applications to discrete Schrödigner operators, and it also applies to various differential operators with constant coefficients and short-range perturbations on Euclidean spaces.
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