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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 for 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.
CONTENTS: 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.
ISBN - 8185931178
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Pages : 226
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