| Softcover ISBN: | 978-0-8218-4864-7 |
| Product Code: | COLL/54.2.S |
| List Price: | $99.00 |
| MAA Member Price: | $89.10 |
| AMS Member Price: | $79.20 |
| eBook ISBN: | 978-1-4704-3200-3 |
| Product Code: | COLL/54.2.E |
| List Price: | $89.00 |
| MAA Member Price: | $80.10 |
| AMS Member Price: | $71.20 |
| Softcover ISBN: | 978-0-8218-4864-7 |
| eBook: ISBN: | 978-1-4704-3200-3 |
| Product Code: | COLL/54.2.S.B |
| List Price: | $188.00 $143.50 |
| MAA Member Price: | $169.20 $129.15 |
| AMS Member Price: | $150.40 $114.80 |
| Softcover ISBN: | 978-0-8218-4864-7 |
| Product Code: | COLL/54.2.S |
| List Price: | $99.00 |
| MAA Member Price: | $89.10 |
| AMS Member Price: | $79.20 |
| eBook ISBN: | 978-1-4704-3200-3 |
| Product Code: | COLL/54.2.E |
| List Price: | $89.00 |
| MAA Member Price: | $80.10 |
| AMS Member Price: | $71.20 |
| Softcover ISBN: | 978-0-8218-4864-7 |
| eBook ISBN: | 978-1-4704-3200-3 |
| Product Code: | COLL/54.2.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; 578 ppMSC: Primary 42; 05; 34; Secondary 47; 30
This two-part 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 one-dimensional 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 9. Rakhmanov’s theorem and related issues
-
Chapter 10. Techniques of spectral analysis
-
Chapter 11. Periodic Verblunsky coefficients
-
Chapter 12. Spectral analysis of specific classes of Verblunsky coefficients
-
Chapter 13. The connection to Jacobi matrices
-
Appendix A. Reader’s guide: Topics and formulae
-
Appendix B. Perspectives
-
Appendix C. Twelve great papers
-
Appendix D. Conjectures and open questions
-
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Requests
This two-part 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 one-dimensional 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 9. Rakhmanov’s theorem and related issues
-
Chapter 10. Techniques of spectral analysis
-
Chapter 11. Periodic Verblunsky coefficients
-
Chapter 12. Spectral analysis of specific classes of Verblunsky coefficients
-
Chapter 13. The connection to Jacobi matrices
-
Appendix A. Reader’s guide: Topics and formulae
-
Appendix B. Perspectives
-
Appendix C. Twelve great papers
-
Appendix D. Conjectures and open questions
