Softcover ISBN:  9780821848630 
Product Code:  COLL/54.1.S 
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eBook ISBN:  9781470431990 
Product Code:  COLL/54.1.E 
List Price:  $89.00 
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Softcover ISBN:  9780821848630 
eBook: ISBN:  9781470431990 
Product Code:  COLL/54.1.S.B 
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AMS Member Price:  $150.40 $114.80 
Softcover ISBN:  9780821848630 
Product Code:  COLL/54.1.S 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470431990 
Product Code:  COLL/54.1.E 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
Softcover ISBN:  9780821848630 
eBook ISBN:  9781470431990 
Product Code:  COLL/54.1.S.B 
List Price:  $188.00 $143.50 
MAA Member Price:  $169.20 $129.15 
AMS Member Price:  $150.40 $114.80 

Book DetailsColloquium PublicationsVolume: 54; 2005; 466 ppMSC: Primary 42; 05; 34; Secondary 47; 30
This twopart volume gives a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of onedimensional Schrödinger operators.
Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegő's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by \(z\) (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line.
The book is suitable for graduate students and researchers interested in analysis.
ReadershipGraduate students and research mathematicians interested in analysis.
This item is also available as part of a set: 
Table of Contents

Chapters

Chapter 1. The Basics

Chapter 2. Szegő’s theorem

Chapter 3. Tools for Geronimus’ theorem

Chapter 4. Matrix representations

Chapter 5. Baxter’s theorem

Chapter 6. The strong Szegő theorem

Chapter 7. Verblunsky coefficients with rapid decay

Chapter 8. The density of zeros


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This twopart volume gives a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of onedimensional Schrödinger operators.
Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegő's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by \(z\) (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line.
The book is suitable for graduate students and researchers interested in analysis.
Graduate students and research mathematicians interested in analysis.

Chapters

Chapter 1. The Basics

Chapter 2. Szegő’s theorem

Chapter 3. Tools for Geronimus’ theorem

Chapter 4. Matrix representations

Chapter 5. Baxter’s theorem

Chapter 6. The strong Szegő theorem

Chapter 7. Verblunsky coefficients with rapid decay

Chapter 8. The density of zeros