Spectral Theory of Dynamical Systems : Second Edition
(1st ed. 2020)
Part of the Texts and Readings in Mathematics series
This book discusses basic topics in the spectral theory of dynamical systems, including two advanced theorems by H.
Helson, W. Parry, and B. Host. It goes on to describe the Ornstein's family of mixing rank-one automorphisms with construction and proof.
Systems of imprimitivity and their relevance to ergodic theory are also examined.
The book also discusses Baire category theorems of ergodic theory, scattered in literature, in a unified way.
Riesz products are considered and used to describe the spectral types and eigenvalues of rank-one automorphisms.
This second edition of the book includes a new chapter "Calculus of Generalized Riesz Products", which discusses the recent work connecting generalized Riesz products, Hardy classes, Banach's problem of simple Lebesgue spectrum in ergodic theory, and flat polynomials.