Texts and Readings in Mathematics

Spectral Theory of Dynamical Systems
M. G. Nadkarni

This book introduces some basic topics in the spectral theory of dynamical systems, but also includes advanced topics such as a theorem due to H. Helson and W. Parry, and another due to B. Host. Moreover, Ornstein's family of mixing rank one automorphisms is described with construction and proof. Systems of imprimitivity, and their relevance to ergodic theory, are discussed. 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.
"Spectral Theory of Dynamical Systems" is the first book devoted exclusively to this subject, moving from introductory material to some topics of current research. The exposition is at a general level and aimed at advanced students and researchers in dynamical systems.

"... compile and communicate in a unique way a lot of mathematics that is of current interest but is not otherwise so readily at hand."
-- Ergodic Theory and Dynamical Systems
1. The Hahn-Hellinger Theorem
2. The Spectral Theorem for Unitary Operators
3. Symmetry and Denseness of the Spectrum
4. Multiplicity and Rank
5. The Skew Product
6. A Theorem of Helson and Parry
7. Probability Measures on the Circle Group
8. Baire Category Theorems of Ergodic Theory
9. Translations of Measures on the Circle
10. B. Host´s Theorem
11. L Eigenvalues of Non-Singular Automorphisms
12. Generalities on Systems of Imprimitivity
13. Dual Systems of Imprimitivity
14. Saturated Subgroups of the Circle Group
15. Riesz Products as Spectral Measures
16. Additional Topics.

Texts and Readings in Mathematics/ 15
Reprint 2011‚ 9789380250212‚ 226 pages‚ paper cover‚ Rs. 300.00