Orthogonal Polynomials on the Unit Circle with quasiperiodic Verblunsky Coefficients have generic purely singular continuous spectrum
Orthogonal Polynomials on the Unit Circle with quasiperiodic Verblunsky Coefficients have generic purely singular continuous spectrum
复制标题
具有准周期Verblunsky系数的单位圆上的正交多项式具有通用的纯奇异连续谱
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Darren C. Ong
中科院分区：
文献类型：
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作者：
Darren C. Ong
作为单位圆上正交多项式Gordon引理的一个应用，我们证明了对于一般的拟周期Verblunsky系数集，相应的双边CMV算子具有纯奇异连续谱.我们使用了与Boshernitzan-Damanik结果相似的论证，该结果建立了离散Schr“odinger算子的相应定理。
As an application of the Gordon lemma for orthogonal polynomials on the unit circle, we prove that for a generic set of quasiperiodic Verblunsky coefficients the corresponding two-sided CMV operator has purely singular continuous spectrum. We use a similar argument to that of the Boshernitzan-Damanik result that establishes the corresponding theorem for the discrete Schr"odinger operator.