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Zero sets, entropy, and pointwise asymptotics of orthogonal polynomials
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2021-03-17 , DOI: 10.1016/j.jfa.2021.109002
Roman Bessonov , Sergey Denisov

Let μ be a measure from Szegő class on the unit circle T and let {fn} be the family of Schur functions generated by μ. In this paper, we prove a version of the classical Szegő's formula, which controls the oscillation of fn on T for all n0. Then, we focus on an analog of Lusin's conjecture for polynomials {φn} orthogonal with respect to measure μ and prove that pointwise convergence of {|φn|} almost everywhere on T is equivalent to a certain condition on zeroes of φn.



中文翻译:

正交多项式的零集,熵和点渐近性

μ为单位圆上Szegő类的度量Ť 然后让 {Fñ}是由μ生成的Schur函数的族。在本文中,我们证明了经典Szegő公式的一个版本,该公式控制着FñŤ 对全部 ñ0。然后,我们将重点放在Lusin多项式猜想的模拟上{φñ}相对于度量μ正交,并证明{|φñ|} 几乎到处都有 Ť 等价于零的某个条件 φñ

更新日期:2021-03-22
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