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Szegő's theorem on Parreau−Widom sets

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Author

Summary, in English

In this paper, we generalize Szegőʼs 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 Szegő 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.

Publishing year

2012

Language

English

Pages

1180-1204

Publication/Series

Advances in Mathematics

Volume

229

Issue

2

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • Szegő integral
  • Eigenvalue sums
  • Parreau–Widom sets

Status

Published

ISBN/ISSN/Other

  • ISSN: 0001-8708