# Journal of Operator Theory

Volume 34, Issue 1, Summer 1995 pp. 177-187.

Spectral analysis for simply characteristic operators by Mourre's method III**Authors**: Gruia Arsu

**Author institution:**Institute of Mathematics, P.O. Box 1-764, RO-70700 Bucharest, ROMANIA

**Summary:**We give a proof of the asymptotic completeness for the wave operators associated to the pair (h(D), h(D) + V_S + V_L) = (H_0, H), where h is a simply characteristic symbol, V_S a short-range perturbation and V_L a long-range potential. The proof is done by using a propagation estimate proved in [2] by means of Mourreâ€™s theory, a characterisation of the orthogonal complement of the ranges of the wave operators in the space of scattering states of H given in [10] and some technical results.

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