论文标题
在频谱类型的等级类型上，一个流量和Banach问题与真实线上的广义Riesz产品的计算
On the spectral type of rank one flows and Banach problem with calculus of generalized Riesz products on the real line
论文作者
论文摘要
结果表明，在$ \ mathbb {r} $上进行的一类Riesz产品类型测量是一种频谱类型的等级。结果，我们将确定某些等级一流的流量具有奇异的频谱。此处介绍的一些结果甚至是$ \ Mathbb {z} $ - Action的新结果。一方面，我们的方法基于Bourgain-klemes-reinhold-peyrière方法的扩展，另一方面，基于将中心限制定理方法扩展到真实线的扩展，从而为Salem-Zygmund中央限制定理提供了新的扩展。我们还扩展了一个rabdalaoui-nadkarni获得的两种广义riesz产品之间的ra子 - 奈克衍生物的公式，以及一种级别的光谱类型的Mahler度量公式，但以弱形式为单位。我们进一步对Banach问题的流程版本提供了肯定的答案，并讨论了与在动力学系统频谱理论中与著名的Banach-Rhoklin问题有关的真实线上平坦三角多项式有关的问题。
It is shown that a certain class of Riesz product type measures on $\mathbb{R}$ is realized a spectral type of rank one flows. As a consequence, we will establish that some class of rank one flows has a singular spectrum. Some of the results presented here are even new for the $\mathbb{Z}$-action. Our method is based, on one hand, on the extension of Bourgain-Klemes-Reinhold-Peyrière method, and on the other hand, on the extension of the Central Limit Theorem approach to the real line which gives a new extension of Salem-Zygmund Central Limit Theorem. We extended also a formula for Radon-Nikodym derivative between two generalized Riesz products obtained by el Abdalaoui-Nadkarni and a formula of Mahler measure of the spectral type of rank one flow but in the weak form. We further present an affirmative answer to the flow version of the Banach problem, and we discuss some issues related to flat trigonometric polynomials on the real line in connection with the famous Banach-Rhoklin problem in the spectral theory of dynamical systems.
