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

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

2005-02-23

arxiv.org/abs/math/0502486v1

Mathematics

Spectral Theory

49 pages

Scientific paper

10.1007/s00222-005-0485-5

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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