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Book Synopsis
This book treats some basic topics in the spectral theory of dynamical systems. The treatment is at a general level, but two more advanced theorems, one by H. Helson and W. Parry and the other by 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 to ergodic theory are 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.

The major change in this edition is that a new chapter titled Calculus of Generalized Riesz Products has been added. This is based on some recent work of the author with El Houcein El Abdalaoui and supplements the material presented elsewhere in the book.

Spectral Theory of Dynamical Systems

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    A Hardback by M.G. Nadkarni

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      Publisher: Jainendra K Jain
      Publication Date: 30/01/2020
      ISBN13: 9789386279811, 978-9386279811
      ISBN10: 9386279819
      Also in:
      Mathematics Differential calculus and equations

      Description

      Book Synopsis
      This book treats some basic topics in the spectral theory of dynamical systems. The treatment is at a general level, but two more advanced theorems, one by H. Helson and W. Parry and the other by 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 to ergodic theory are 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.

      The major change in this edition is that a new chapter titled Calculus of Generalized Riesz Products has been added. This is based on some recent work of the author with El Houcein El Abdalaoui and supplements the material presented elsewhere in the book.

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