Jost Functions and Jost Solutions for Jacobi Matrices, I. A Necessary and Sufficient Condition for Szego Asymptotics
Spectral Theory
2014-12-30 v1 Classical Analysis and ODEs
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 convergence of Szeg\H{o} asymptotics on the spectrum.
Keywords
Cite
@article{arxiv.math/0502486,
title = {Jost Functions and Jost Solutions for Jacobi Matrices, I. A Necessary and Sufficient Condition for Szego Asymptotics},
author = {David Damanik and Barry Simon},
journal= {arXiv preprint arXiv:math/0502486},
year = {2014}
}
Comments
49 pages