Finite Gap Jacobi Matrices: An Announcement

Abstract

We consider Jacobi matrices whose essential spectrum is a finite union of closed intervals. We focus on Szego's theorem, Jost solutions, and Szego asymptotics for this situation. This announcement describes talks the authors gave at OPSFA 2007.

17 pages, 2 figures

References in corpus (3)

• Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States
• Eigenvalue bounds in the gaps of Schrodinger operators and Jacobi matrices
• Remark on the paper "Asymptotic behavior of polynomials orthonormal on a homogeneous set"

Cited by in corpus (4)

• On the Direct Cauchy Theorem in Widom Domains: Positive and Negative Examples
• Orthogonal polynomials on several intervals: accumulation points of recurrence coefficients and of zeros
• Szego's theorem on Parreau-Widom sets
• Finite Gap Jacobi Matrices, I. The Isospectral Torus