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About this product
- DescriptionThis book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polymials, 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 w 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 polymials for measures supported on a finite number of intervals on the real line. In addition to the Szego and Killip-Simon theorems for orthogonal polymials on the unit circle (OPUC) and orthogonal polymials 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.
- Author BiographyBarry Simon is the IBM Professor of Mathematics and Theoretical Physics at the California Institute of Technology. His books include Methods of Modern Mathematical Physics and Orthogonal Polynomials on the Unit Circle .
- Author(s)Barry Simon
- PublisherPrinceton University Press
- Date of Publication08/11/2010
- Series TitlePorter Lectures
- Place of PublicationNew Jersey
- Country of PublicationUnited States
- ImprintPrinceton University Press
- Content Note8 line illus.
- Weight1085 g
- Width152 mm
- Height229 mm
- Spine38 mm
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