Spectral theory of dynamical systems [electronic resource] / M. G. Nadkarni.

Nadkarni, M. G.
Call Number
515.352
Author
Nadkarni, M. G.
Title
Spectral theory of dynamical systems M. G. Nadkarni.
Edition
1st ed.
Physical Description
1 online resource (230 pages)
Series
Texts and Readings in Mathematics ; 15
Contents
Spectral theory of dynamical systems -- Contents -- Preface -- Chapter 1: The Hahn-Hellinger Theorem -- Chapter 2: The Spectral Theorem for Unitary Operators -- Chapter 3: Symmetry and Denseness of the Spectrum -- Chapter 4: Multiplicity and Rank -- Chapter 5: The Skew Product -- Chapter 6: A Theorem of Helson and Parry -- Chapter 7: Probability Measures on the Circle Group -- Chapter 8: Baire Category Theorems of Ergodic Theory -- Chapter 9: Translations of Measures on the Circle -- Chapter 10: B. Host's Theorem -- Chapter 11: L∞‡ Eigenvalues of Non-Singular Automorphisms -- Chapter 12: Generalities on Systems of Imprimitivity -- Chapter 13: Dual Systems of Imprimitivity -- Chapter 14: Saturated Subgroups of the Circle Group -- Chapter 15: Riesz Products As Spectral Measures -- Chapter 16: Additional Topics -- References -- Index.
Summary
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.
Subject
MATHEMATICS / Differential Equations / General.
MATHEMATICS / Mathematical Analysis.
MATHEMATICS / Functional Analysis.
Electronic books.
Multimedia
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$a Texts and Readings in Mathematics ; $v 15
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$a Spectral theory of dynamical systems -- Contents -- Preface -- Chapter 1: The Hahn-Hellinger Theorem -- Chapter 2: The Spectral Theorem for Unitary Operators -- Chapter 3: Symmetry and Denseness of the Spectrum -- Chapter 4: Multiplicity and Rank -- Chapter 5: The Skew Product -- Chapter 6: A Theorem of Helson and Parry -- Chapter 7: Probability Measures on the Circle Group -- Chapter 8: Baire Category Theorems of Ergodic Theory -- Chapter 9: Translations of Measures on the Circle -- Chapter 10: B. Host's Theorem -- Chapter 11: L∞‡ Eigenvalues of Non-Singular Automorphisms -- Chapter 12: Generalities on Systems of Imprimitivity -- Chapter 13: Dual Systems of Imprimitivity -- Chapter 14: Saturated Subgroups of the Circle Group -- Chapter 15: Riesz Products As Spectral Measures -- Chapter 16: Additional Topics -- References -- Index.
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$a This book introduces some basic topics in the spectral theory of dynamical systems, but also includes advanced topics such as a theorem due to H. Helson and W. Parry, and another due to B. Host. Moreover, Ornstein's family of mixing rank one automorphisms is described with construction and proof. Systems of imprimitivity, and their relevance to ergodic theory, are discussed. Baire category theorems of ergodic theory, scattered in the literature, are derived in a unified way. Riesz products are considered, and they are used to describe the spectral types and eigenvalues of rank one automorphisms.
538
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$a MATHEMATICS / Mathematical Analysis. $2 bisacsh
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$a MATHEMATICS / Functional Analysis. $2 bisacsh
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$a Electronic books.
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No Reviews to Display
Summary
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.
Contents
Spectral theory of dynamical systems -- Contents -- Preface -- Chapter 1: The Hahn-Hellinger Theorem -- Chapter 2: The Spectral Theorem for Unitary Operators -- Chapter 3: Symmetry and Denseness of the Spectrum -- Chapter 4: Multiplicity and Rank -- Chapter 5: The Skew Product -- Chapter 6: A Theorem of Helson and Parry -- Chapter 7: Probability Measures on the Circle Group -- Chapter 8: Baire Category Theorems of Ergodic Theory -- Chapter 9: Translations of Measures on the Circle -- Chapter 10: B. Host's Theorem -- Chapter 11: L∞‡ Eigenvalues of Non-Singular Automorphisms -- Chapter 12: Generalities on Systems of Imprimitivity -- Chapter 13: Dual Systems of Imprimitivity -- Chapter 14: Saturated Subgroups of the Circle Group -- Chapter 15: Riesz Products As Spectral Measures -- Chapter 16: Additional Topics -- References -- Index.
Subject
MATHEMATICS / Differential Equations / General.
MATHEMATICS / Mathematical Analysis.
MATHEMATICS / Functional Analysis.
Electronic books.
Multimedia