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Orthogonal Polynomials on the Unit Circle: Part 2: Spectral Theory
 
Barry Simon California Institute of Technology, Pasadena, CA
Orthogonal Polynomials on the Unit Circle
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
Orthogonal Polynomials on the Unit Circle
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Orthogonal Polynomials on the Unit Circle: Part 2: Spectral Theory
Barry Simon California Institute of Technology, Pasadena, CA
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 Details
     
     
    Colloquium Publications
    Volume: 542005; 578 pp
    MSC: 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.

    Readership

    Graduate 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 542005; 578 pp
MSC: 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.

Readership

Graduate students and research mathematicians interested in analysis.

This item is also available as part of a set:
  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.