We study the spectral measures associated with pattern sequences of general degrees. They are either discrete, purely singular or absolutely continuous. We obtain a necessary and sufficient condition for the discreteness. We also obtain a sufficient condition to be absolutely continuous or to be the Lebesgue measure.

中文翻译：

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一般度模式序列的光谱特性

我们研究了与一般度模式序列相关的频谱度量。它们要么是离散的、纯奇异的，要么是绝对连续的。我们得到了离散性的充分必要条件。我们还获得了绝对连续或 Lebesgue 测度的充分条件。