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Spectral theory of dynamical systems

Nadkarni, Mahendra.

Spectral theory of dynamical systems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Spectral theory of dynamical systemsby Mahendra Nadkarni.
Author:	Nadkarni, Mahendra.
Published:	Singapore :Springer Singapore :2020.
Description:	xiii, 223 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Spectral theory (Mathematics)
Online resource:	https://doi.org/10.1007/978-981-15-6225-9
ISBN:	9789811562259$q(electronic bk.)

Spectral theory of dynamical systems
Nadkarni, Mahendra.

Spectral theory of dynamical systems[electronic resource] /by Mahendra Nadkarni. - Second edition - Singapore :Springer Singapore :2020. - xiii, 223 p. :ill., digital ;24 cm. - Texts and readings in mathematics,152366-8717 ;. - Texts and readings in mathematics ;74..

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.

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.

ISBN: 9789811562259$q(electronic bk.)

Standard No.: 10.1007/978-981-15-6225-9doiSubjects--Topical Terms:

182365
Spectral theory (Mathematics)

LC Class. No.: QA313 / .N335 2020

Dewey Class. No.: 515.39

Spectral theory of dynamical systems
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100 1 $a Nadkarni, Mahendra. $3 876417
245 1 0 $a Spectral theory of dynamical systems $h [electronic resource] / $c by Mahendra Nadkarni.
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300 $a xiii, 223 p. : $b ill., digital ; $c 24 cm.
490 1 $a Texts and readings in mathematics, $x 2366-8717 ; $v 15
505 0 $a 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.
520 $a 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.
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650 2 4 $a Operator Theory. $3 274795
650 2 4 $a Topology. $3 185965
650 2 4 $a Group Theory and Generalizations. $3 274819
650 2 4 $a Field Theory and Polynomials. $3 274058
650 2 4 $a Statistical Physics and Dynamical Systems. $3 760415
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