Szego's theorem on Parreau-Widom sets
Classical Analysis and ODEs
2019-10-29 v1 Spectral Theory
Abstract
In this paper, we generalize Szego's theorem for orthogonal polynomials on the real line to infinite gap sets of Parreau-Widom type. This notion includes Cantor sets of positive measure. The Szego condition involves the equilibrium measure which is shown to be absolutely continuous. Our approach builds on a canonical factorization of the M-function and the covering space formalism of Sodin-Yuditskii.
Cite
@article{arxiv.1104.1915,
title = {Szego's theorem on Parreau-Widom sets},
author = {Jacob S. Christiansen},
journal= {arXiv preprint arXiv:1104.1915},
year = {2019}
}
Comments
19 pages