Szego's theorem on Parreau-Widom sets

Details Szego's theorem on Parreau-Widom sets Szego's theorem on Parreau-Widom sets

2011-04-11

arxiv.org/abs/1104.1915v1

Mathematics

Classical Analysis and ODEs

19 pages

Scientific paper

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.

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