A Singular Riesz Product in the Nevai Class and Inner Functions with the Schur Parameters in ∩p>2 l |
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Authors: | Sergei Khrushchev |
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Affiliation: | Dolgoozernaya ul. 6, Block 1, Apt. 116, 197373, St. Petersburg, Russia |
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Abstract: | There exist singular Riesz products dσ=∏∞κ=1 (1+Re(ακζnκ)) on the unit circle with the parameters (an)n0 of orthogonal polynomials in L2(dσ) satisfying ∑∞n=0 |an|p<+∞ for every p, p>2. The Schur parameters of the inner factor of the Cauchy integral ∫ (ζ−z)−1 dσ(ζ), σ being such a Riesz product, belong to ∩p>2 lp. |
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Keywords: | Schur parameters orthogonal polynomials Blaschke product Riesz products |
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