自共形测度的对数Fourier衰减
Logarithmic Fourier decay for self conformal measures
摘要：
我们证明了在$\mathbb{R}$上的自共形测度的傅里叶变换在无穷远处以对数速率衰减到$0$，除非以下情况成立：基础IFS光滑共轭到IFS，该IFS既线性作用于其吸引子，又通过不是丢番图的尺度收缩。我们的关键技术成果是Benoist-Quint（2016）的一个有效版本的局部极限定理，适用于具有中等偏差的上循环，这是独立的兴趣。
英文摘要：
We prove that the Fourier transform of a self conformal measure on $\mathbb{R}$ decays to $0$ at infinity at a logarithmic rate, unless the following holds: The underlying IFS is smoothly conjugated to an IFS that both acts linearly on its attractor and contracts by scales that are not Diophantine. Our key technical result is an effective version of a local limit Theorem for cocycles with moderate deviations due to Benoist-Quint (2016), that is of independent interest.
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