A local criterion for the existence of wave operators

Within the framework of the theory of nuclear perturbations of self-adjoint operators, conditions are given for the existence of wave operators corresponding to a given part of the spectrum. Conditions are given separately for the existence of weak wave operators, for them to be isometric and for them to be complete. A number of new criteria for the existence of wave operators corresponding to the whole spectrum are found on the basis of the general theorems that are obtained. These criteria are convenient in applications to concrete problems of scattering theory.