Rafael Tiedra de Aldecoa: Commutator methods for unitary operators

We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singular continuous spectrum and to the local finiteness of point spectrum. Some applications for perturbations of the Schroedinger evolution and for cocycles over irrational rotations will be presented.