Jost Functions and Jost Solutions for Jacobi Matrices, I. A Necessary and Sufficient Condition for Szego Asymptotics

Abstract

We provide necessary and sufficient conditions for a Jacobi matrix to produce orthogonal polynomials with Szegő asymptotics off the real axis. A key idea is to prove the equivalence of Szegő asymptotics and of Jost asymptotics for the Jost solution. We also prove $L^2$ convergence of Szegő asymptotics on the spectrum.

49 pages

References in corpus (3)

• Sum Rules and the Szego Condition for Orthogonal Polynomials on the Real Line
• Variational Estimates for Discrete Schrödinger Operators with Potentials of Indefinite Sign
• Jost Functions and Jost Solutions for Jacobi Matrices, II. Decay and Analyticity

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