Spectral theory of dynamical systems / Mahendra Nadkarni.

Spectral theory of dynamical systems / Mahendra Nadkarni.

Second edition.

9789811562259 (electronic book)
9811562253 (electronic book)
9789811562242

Singapore : Springer, [2020]

English

1 online resource

10.1007/978-981-15-6225-9 doi
10.1007/978-981-15-6

QA313 .S64 2020

515.39

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, Ornsteins 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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