Weak limits of powers, simple spectrum of symmetric products, and rank-one mixing constructions

Abstract

A class of automorphisms of the Lebesgue space such that their symmetric powers have simple spectrum is considered. In the framework of rank-one constructions mixing automorphisms with this property are constructed. The paper also contains results on weak limits, the local rank, and the spectral multiplicity of powers of automorphisms. Spectral properties of the stochastic Chacon automorphism are discussed.Bibliography: 23 titles.