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 --;References.
This book treats some basic topics in the spectral theory of dynamical systems, where by a dynamical system we mean a measure space on which a group of automorphisms acts preserving the sets of measure zero.