Szegö's theorem on Parreau-Widom sets

Jacob Stordal Christiansen

doi:10.1016/j.aim.2011.09.012

Szegö's theorem on Parreau-Widom sets

Jacob Stordal Christiansen

Department of Mathematical Sciences

17 Citations (Scopus)

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 in turn is absolutely continuous. Our approach builds on a canonical factorization of the M-function and the covering space formalism of Sodin–Yuditskii.

Original language	English
Journal	Advances in Mathematics
Volume	229
Issue number	2
Pages (from-to)	1180-1204
Number of pages	25
ISSN	0001-8708
DOIs	https://doi.org/10.1016/j.aim.2011.09.012
Publication status	Published - 2012

Keywords

Faculty of Science

Access to Document

10.1016/j.aim.2011.09.012

Cite this

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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 in turn is absolutely continuous. Our approach builds on a canonical factorization of the M-function and the covering space formalism of Sodin–Yuditskii.",

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