Generalized wave operators: dynamical and stationary cases and divergence problem

Abstract: Ideas and results of the generalized wave operator theory for dynamical and stationary cases are developed further and exact expressions for generalized scattering operators are obtained for wide classes of differential equations. New results on the structure of the generalized scattering operators are derived. Interesting interrelations between dynamical and stationary cases are found for radial Schr\"odinger and Dirac equations, and for Dirac-type equations as well. For some important examples we explain why the well-known divergences in the higher order approximations of the scattering matrices do not appear in the "generalized wave operator" approach.