论文标题
复杂平面上的自相似度量的傅立叶衰变
Fourier decay of self-similar measures on the complex plane
论文作者
论文摘要
我们证明，复杂平面上的自相似度量的傅立叶变换在非常稀疏的频率之外具有快速的衰减，并具有定量估计值，扩展了R. Kaufman在实际线上获得的结果，首先是R. Kaufman，后来又具有定量界限，由第一作者和P. Shmerkin和P. Shmerkin。同样，我们得出了有关这些措施的相关维度和霜冻指数的几种应用程序。此外，我们在$ \ mathbb {r}^n，$ a $ n \ ge3上提出了特定情况的概括。
We prove that the Fourier transform of self-similar measures on the complex plane has fast decay outside of a very sparse set of frequencies, with quantitative estimates, extending the results obtained in the real line, first by R. Kaufman, and later, with quantitative bounds, by the first author and P. Shmerkin. Also we derive several applications concerning correlation dimension and Frostman exponent of these measures. Furthermore, we present a generalization for a particular case on $\mathbb{R}^n,$ with $n\ge3.$
