Logarithmic Fourier decay for self conformal measures
Logarithmic Fourier decay for self conformal measures
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DOI：
10.1112/jlms.12608
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发表时间：
2021-09
期刊：
影响因子：
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通讯作者：
A. Algom;F. Rodriguez Hertz;Zhiren Wang
中科院分区：
文献类型：
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作者：
A. Algom;F. Rodriguez Hertz;Zhiren Wang
我们证明了R$\mathbb{R}上的自共形测度的傅立叶变换以对数速率在无穷远处衰减到0，除非下列条件成立：下标的迭代函数系统光滑地共轭到一个既线性作用于吸引子又按非丢番图的尺度压缩的迭代函数系统.我们的关键技术结果是由Benoist-Quint(2016)得到的具有中等偏差的余循环的局部极限定理的有效版本，这是独立感兴趣的。
We prove that the Fourier transform of a self conformal measure on R$\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.