05-79 David Damanik, Barry Simon

Jost Functions and Jost Solutions for Jacobi Matrices, I. A Necessary and Sufficient Condition for Szego Asymptotics (113K, LaTeX) Feb 23, 05

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

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