Nadkarni M Spectral Theory of Dynamical Systems 2ed 2020 torrent

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This book discusses basic topics in the spectral theory of dynamical systems. It also includes two advanced theorems, one by H. Helson and W. Parry, and another by B. Host. Moreover, Ornstein’s family of mixing rank-one automorphisms is given with construction and proof. Systems of imprimitivity and their relevance to ergodic theory are also examined. Baire category theorems of ergodic theory, scattered in literature, are discussed in a unified way in the book. Riesz products are introduced and applied to describe the spectral types and eigenvalues of rank-one automorphisms. Lastly, the second edition 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.
Table of contents
The Hahn-Hellinger Theorem
The Spectral Theorem for Unitary Operators
Symmetry and Denseness of the Spectrum
Multiplicity and Rank
The Skew Product
A Theorem of Helson and Parry
Probability Measures on the Circle Group
Baire Category Theorems of Ergodic Theory
Translations of Measures on the Circle
B. Host’s Theorem
L∞ Eigenvalues of Non-Singular Automorphisms
Generalities on Systems of Imprimitivity
Dual Systems of Imprimitivity
Saturated Subgroups of the Circle Group
Riesz Products As Spectral Measures
Additional Topics
Calculus of Generalized Riesz Products