Regularity and the Cesàro–Nevai class
Journal of Approximation Theory
Monotone Jacobi parameters and non-Szegő weights
Journal of Approximation Theory
Poisson brackets of orthogonal polynomials
Journal of Approximation Theory
Finite gap Jacobi matrices: An announcement
Journal of Computational and Applied Mathematics
Szegő asymptotics for matrix-valued measures with countably many bound states
Journal of Approximation Theory
Asymptotics of the L2 norm of derivatives of OPUC
Journal of Approximation Theory
Journal of Approximation Theory
Journal of Approximation Theory
Full length article: Orthogonal polynomials of the R-linear generalized minimal residual method
Journal of Approximation Theory
Journal of Approximation Theory
Full length article: Orthogonal polynomials on the unit circle and chain sequences
Journal of Approximation Theory
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This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gbor 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.