A Singular Riesz Product in the Nevai Class and Inner Functions with the Schur Parameters in ∩p>2 l期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A Singular Riesz Product in the Nevai Class and Inner Functions with the Schur Parameters in ∩_p>2 l

Authors:	Sergei Khrushchev

Institution:	Dolgoozernaya ul. 6, Block 1, Apt. 116, 197373, St. Petersburg, Russia

Abstract:	There exist singular Riesz products dσ=∏^∞_κ=1 (1+Re(α_κζ^n_κ)) on the unit circle with the parameters (a_n)_n0 of orthogonal polynomials in L²(dσ) satisfying ∑^∞_n=0 \|a_n\|^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 l^p.

Keywords:	Schur parameters orthogonal polynomials Blaschke product Riesz products
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