Jost Functions and Jost Solutions for Jacobi Matrices, I. A Necessary and Sufficient Condition for Szego Asymptotics
arXiv:math/0502486 · doi:10.1007/s00222-005-0485-5
Abstract
We provide necessary and sufficient conditions for a Jacobi matrix to produce orthogonal polynomials with SzegÅ asymptotics off the real axis. A key idea is to prove the equivalence of SzegÅ asymptotics and of Jost asymptotics for the Jost solution. We also prove $L^2$ convergence of SzegÅ asymptotics on the spectrum.
49 pages