Orthogonal Polynomials on the Unit Circle: Spectral theory, Part 2

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American Mathematical Soc., 2005 - Science - 1044 pages
Presents an overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. This book discusses topics such as asymptotics of Toeplitz determinants (Szego's theorems), and limit theorems for the density of the zeros of orthogonal polynomials.
 

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Contents

Preface to Part 1
xi
Notation
xvii
Rakhmanovs Theorem and Related Issues
467
Techniques of Spectral Analysis
545
The Basics 1
580
Periodic Verblunsky Coefficients
709
Spectral Analysis of Specific Classes
817
The Connection to Jacobi Matrices
871
Topics and Formulae
945
Appendix B Perspectives
971
Conjectures and Open Questions
981
Szegos Theorem 109
1014
Author Index
1031
Subject Index
1039
Matrix Representations 251
1040
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About the author (2005)

Barry Simon is IBM Professor of Mathematics and Theoretical Physics at the California Institute of Technology.

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