Spectral Theory of Dynamical Systems

This book treats some basic topics in the spectral theory of dynamical systems. The treatment is at a general level, but even here, two theorems which are not on the surface, one due to H. Helson and W. Parry, and the other due to B. Host, are presented. Moreover, Ornstein’s family of mixing rank one automorphisms is described with construction and proof. Systems of imprimitivity and their relevance to Ergodic theory is discussed, and Baire category theorems of Ergodic theory, scattered in the literature, are derived in a unified way. Riesz products are considered, and they are used to describe the spectral types and eigenvalues of rank one automorphisms.