We prove a lower bound on the spacing of zeros of paraorthogonal polynomials on the unit circle, based on continuity of the underlying measure as measured by Hausdorff dimensions. We complement this with the analog of the result from Breuer (2011) showing that clock spacing holds even for certain singular continuous measures.

中文翻译：

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关于奇异测度的正交多项式零点的间距

基于由Hausdorff尺寸测量的基础度量的连续性，我们证明了单位圆上正交多项式零点间距的下限。我们用来自Breuer（2011）的结果类似物来补充这一点，该结果表明即使对于某些奇异的连续测量，时钟间隔也成立。