STRONG NONRESONANCE OF SCHRODINGER-OPERATORS AND AN AVERAGING THEOREM

We prove that linear Schrodinger operators -Delta + q on a torus or on a bounded smooth domain in R(d) considered with Dirichlet boundary conditions, have a strongly nonresonant spectrum for any potential q of generic type (generic in the sense of Kolmogorov measure). As a consequence, a Krylov-Bogolubov averaging theorem holds for nonlinear perturbations of the corresponding Schrodinger evolution equations.