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＜E-Book＞
Spectral Theory of Dynamical Systems : Second Edition / by Mahendra Nadkarni
(Texts and Readings in Mathematics. ISSN:23668725 ; 15)

Edition	1st ed. 2020.
Publisher	(Singapore : Springer Nature Singapore : Imprint: Springer)
Year	2020
Size	XIII, 223 p. 2 illus : online resource
Authors	*Nadkarni, Mahendra author SpringerLink (Online service)
Subjects	LCSH:Dynamical systems LCSH:Operator theory LCSH:Topology LCSH:Group theory LCSH:Algebraic fields LCSH:Polynomials LCSH:Mathematical physics FREE:Dynamical Systems FREE:Operator Theory FREE:Topology FREE:Group Theory and Generalizations FREE:Field Theory and Polynomials FREE:Theoretical, Mathematical and Computational Physics
Notes	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 HTTP:URL=https://doi.org/10.1007/978-981-15-6225-9

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