Szegő's theorem on Parreau−Widom sets

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Sammanfattning

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.
Originalspråkengelska
Sidor (från-till)1180-1204
TidskriftAdvances in Mathematics
Volym229
Utgåva2
DOI
StatusPublished - 2012
Externt publiceradJa

Ämnesklassifikation (UKÄ)

  • Matematik

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