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Spectral Theory of Dynamical Systems: Second Edition: 15 (Texts and Readings in Mathematics, 15) - Softcover

Nadkarni, Mahendra

 
9789811562273: Spectral Theory of Dynamical Systems: Second Edition: 15 (Texts and Readings in Mathematics, 15)
Softcover
ISBN 10: 981156227X ISBN 13: 9789811562273
Publisher: Springer, 2021

Synopsis

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.

"synopsis" may belong to another edition of this title.

About the Author

Mahendra Nadkarni is Emeritus Professor of mathematics at the University of Mumbai, India. He earned his M.Sc. degree in Mathematics from the University of Mumbai in 1960 and Ph.D. in applied mathematics from Brown University in1965. His research and pedagogic interests are in the areas of ergodic theory, harmonic analysis and probability theory in which he has scholarly publications including a book titled Basic Ergodic Theory. He is Fellow of the Indian National Science Academy, New Delhi, and, the Indian Academy of Sciences, Bengaluru. He has taught at the Indian Statistical Institute, Kolkata; the University of Minnesota, Minneapolis; Chennai Mathematical Institute, Chennai; the Indian Institute of Technology Indore; the Indian Institute of Technology Kanpur; Center of Excellence in Basic Sciences, Mumbai; and had visiting appointments at McGill University, Universities of York and Toronto in Canada. 

From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2021
Language
English
ISBN 10 
981156227X
ISBN 13 
9789811562273
Binding
Paperback
Edition number
1
Number of pages
236