Description

This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gabor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first book-length treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line. In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC.

Szegő's Theorem and Its Descendants: Spectral Theory for L2 Perturbations of Orthogonal Polynomials

Product form

£120.60

Includes FREE delivery
RRP: £134.00 You save £13.40 (10%)
Usually despatched within 5 days
Hardback by Barry Simon

1 in stock

Short Description:

This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from... Read more

    Publisher: Princeton University Press
    Publication Date: 28/11/2010
    ISBN13: 9780691147048, 978-0691147048
    ISBN10: 0691147043

    Number of Pages: 664

    Non Fiction , Mathematics & Science , Education

    Description

    This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gabor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first book-length treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line. In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC.

    Customer Reviews

    Be the first to write a review
    0%
    (0)
    0%
    (0)
    0%
    (0)
    0%
    (0)
    0%
    (0)

    Recently viewed products

    © 2024 Book Curl,

      • American Express
      • Apple Pay
      • Diners Club
      • Discover
      • Google Pay
      • Maestro
      • Mastercard
      • PayPal
      • Shop Pay
      • Union Pay
      • Visa

      Login

      Forgot your password?

      Don't have an account yet?
      Create account