Cesàro Asymptotics for Orthogonal Polynomials on the Unit Circle and Classes of Measures |
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Authors: | Leonid Golinskii Sergei Khrushchev |
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Affiliation: | Mathematics Division, B. Verkin Institute for Low Temperature Physics and Engineering, 47 Lenin Avenue, 61103, Kharkov, Ukrainef1;Department of Mathematics, Atilim University, 06836 Incek, Ankara, Turkey, f2 |
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Abstract: | The convergence in L2() of the even approximants of the Wall continued fractions is extended to the Cesàro–Nevai class CN, which is defined as the class of probability measures σ with limn→∞ ∑n−1k=0 |ak|=0, {an}n0 being the Geronimus parameters of σ. We show that CN contains universal measures, that is, probability measures for which the sequence {|n|2 dσ}n0 is dense in the set of all probability measures equipped with the weak-* topology. We also consider the “opposite” Szeg class which consists of measures with ∑∞n=0 (1−|an|2)1/2<∞ and describe it in terms of Hessenberg matrices. |
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Keywords: | unit circle orthogonal polynomials Schur functions Schur parameters strong summability |
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