Commutator methods for the spectral analysis of uniquely ergodic dynamical systems
Commutator methods for the spectral analysis of uniquely ergodic dynamical systems
复制标题
用于独特遍历动力系统谱分析的换向器方法
DOI：
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发表时间：
2012
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通讯作者：
R. T. Aldecoa
中科院分区：
文献类型：
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作者：
R. T. Aldecoa
本文提出了一种基于交换子方法的唯一遍历动力系统的谱分析方法。当适用时，它导致相应的酉算子的谱的绝对连续性。作为一个例子，我们考虑时变的horocycle流，斜产品的翻译和Furstenberg变换。对于时间变化的horocycle流，我们得到绝对连续性的假设弱于那些被发现在文献中，和斜产品的翻译和Furstenberg变换，我们得到可数勒贝格谱的假设下，以前没有在文献中。
We present a method, based on commutator methods, for the spectral analysis of uniquely ergodic dynamical systems. When applicable, it leads to the absolute continuity of the spectrum of the corresponding unitary operators. As an illustration, we consider time changes of horocycle flows, skew products over translations and Furstenberg transformations. For time changes of horocycle flows we obtain absolute continuity under assumptions weaker than those to be found in the literature, and for skew products over translations and Furstenberg transformations we obtain countable Lebesgue spectrum under assumptions not previously covered in the literature.