Spectral theory of dynamical systems
著者
書誌事項
Spectral theory of dynamical systems
（Birkhäuser advanced texts : Basler Lehrbücher / edited by Herbert Amann, Hanspeter Kraft）
Birkhauser, 1998
- : sz
- : us
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注記
Includes bibliographical references (p. [171]-178) and index
内容説明・目次
内容説明
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.
目次
- 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 special measures
- additional topics.
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