论文标题
部分可观测时空混沌系统的无模型预测
Fourier decay of self-similar measures and self-similar sets of uniqueness
论文作者
论文摘要
在本文中，我们研究了对R的自相似度量的傅立叶变换。我们提供了一些自相似度量的傅立叶变换的定量衰减率。我们的方法基于在数字字段中的晶格和双磷酸近似的随机步行。我们还完全确定了所有相似的集合，这些集合是独特性的集合。这概括了塞勒姆和Zygmund的经典结果。
In this paper, we investigate the Fourier transform of self-similar measures on R. We provide quantitative decay rates of Fourier transform of some self-similar measures. Our method is based on random walks on lattices and Diophantine approximation in number fields. We also completely identify all self-similar sets which are sets of uniqueness. This generalizes a classical result of Salem and Zygmund.
