Stationary scattering theory on manifolds, II

Based on our previous study [IS2] we develop fully the stationary scattering theory for the Schrodinger operator on a manifold possessing an escape function. A particular class of examples are manifolds with Euclidean and/or hyperbolic ends, possibly with unbounded and non-smooth obstacles. We develop the theory largely along the classical lines [Sa, Co] and derive in particular WKB- asymptotics of appropriate generalized eigenfunctions. As an application we solve a conjecture of [HPW] on cross-ends transmissions in its natural and strong form within the framework of our theory.