It is shown that under fairly weak conditions on the measure the orthonormal polynomials have almost everywhere oscillatory behavior. A simple lower bound for the amplitude of oscillation is also given in terms of the measure and the equilibrium density of the support. This bound is also shown to be exact in some situations.

中文翻译：

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正交多项式的振荡行为

结果表明，在测量的相当弱的条件下，正交多项式几乎在任何地方都具有振荡行为。还根据支撑物的测量和平衡密度给出了振荡幅度的简单下限。在某些情况下，这个界限也被证明是准确的。