Szegő's Theorem and Its Descendants : : Spectral Theory for L‹sup›2‹/sup› Perturbations of Orthogonal Polynomials / / Barry Simon.

• Superior document: Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013
• VerfasserIn: Simon, Barry,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2010]; ©2011
• Year of Publication: 2010
• Edition: Course Book
• Language: English
• Series: Porter Lectures ; 6
• Physical Description: 1 online resource (664 p.) :; 8 line illus.
• Other title: Frontmatter --; Contents --; Preface --; Chapter One. Gems of Spectral Theory --; Chapter Two. Szegő's Theorem --; Chapter Three The Killip-Simon Theorem: Szegő for OPRL --; Chapter Four. Sum Rules and Consequences for Matrix Orthogonal Polynomials --; Chapter Five. Periodic OPRL --; Chapter Six. Toda Flows and Symplectic Structures --; Chapter Seven. Right Limits --; Chapter Eight. Szegő and Killip-Simon Theorems for Periodic OPRL --; Chapter Nine. Szegő's Theorem for Finite Gap OPRL --; Chapter Ten. A.C. Spectrum for Bethe-Cayley Trees --; Bibliography --; Author Index --; Subject Index
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400837052; 9783110442502
• DOI: 10.1515/9781400837052?locatt=mode:legacy
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Barry Simon.

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