Szegö's theorem on Parreau-Widom sets
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Szegö's theorem on Parreau-Widom sets. / Christiansen, Jacob Stordal.
In: Advances in Mathematics, Vol. 229, No. 2, 2012, p. 1180-1204.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Szegö's theorem on Parreau-Widom sets
AU - Christiansen, Jacob Stordal
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - Faculty of Science
KW - Mathematics
U2 - 10.1016/j.aim.2011.09.012
DO - 10.1016/j.aim.2011.09.012
M3 - Journal article
VL - 229
SP - 1180
EP - 1204
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
IS - 2
ER -
ID: 35345929