Cesàro Asymptotics for Orthogonal Polynomials on the Unit Circle and Classes of Measures
Cesàro Asymptotics for Orthogonal Polynomials on the Unit Circle and Classes of Measures
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单位圆和测度类上正交多项式的 Cesàro 渐近
DOI：
10.1006/jath.2001.3655
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
S. Khrushchev
中科院分区：
文献类型：
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作者：
L. Golinskii;S. Khrushchev
将Wall连分式的偶逼近在L2（T）中的收敛性推广到塞萨罗？Nevai类CN，定义为概率测度类？在Limn？∞1n？你好吗？1k=0| AK| =0，{an}n？0是？的Geronimus参数。我们证明了CN包含泛测度，即概率测度，序列{|? n| 2D？你好吗？0在所有具有弱-* 拓扑的概率测度的集合中是稠密的。我们还考虑“相反”Szego？类，其中包含的措施与？∞n=0（1？|一个|2）1/2<∞，并用Hessenberg矩阵描述。
The convergence in L2(T) of the even approximants of the Wall continued fractions is extended to the Cesaro?Nevai class CN, which is defined as the class of probability measures ? with limn?∞1n?n?1k=0|ak|=0, {an}n?0 being the Geronimus parameters of ?. We show that CN contains universal measures, that is, probability measures for which the sequence {|?n|2d?}n?0 is dense in the set of all probability measures equipped with the weak-* topology. We also consider the “opposite” Szego? class which consists of measures with ?∞n=0(1?|an|2)1/2<∞ and describe it in terms of Hessenberg matrices.