Weakly Wandering Vectors for Unitary Actions of Commutative Groups

We extend the main result of [V. Bergelson, I. Kornfeld, and B. Mityagin, Proc. Amer. Math. Soc.119 (1993), 1127-1134.] to more general commutative group actions satisfying different mixing conditions. The more general setup required introduction of new techniques based on spectral theory as well as refinement of those used in that paper.