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Spectral Theory of Dynamical Systems
M. G. Nadkarni, University of Mumbai, India
A publication of Hindustan Book Agency.
cover
Hindustan Book Agency
2011; 226 pp; softcover
ISBN-10: 93-80250-21-5
ISBN-13: 978-93-80250-21-2
List Price: US$40
Member Price: US$32
Order Code: HIN/54
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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 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.

A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

Readership

General audience interested in analysis.

Reviews

"... compile and communicate in a unique way a lot of mathematics that is of current interest but is not otherwise so readily at hand."

-- Ergodic Theory and Dynamical Systems

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
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