极限分布在$q$ - CLT中对于$q \ge 1$不能有紧支集
Limit distribution in the $q$-CLT for $q \ge 1$ can not have a compact support
摘要：
在最近的一份文件中Hilhorst \cite{Hilhorst2010}说明，$q$ -傅立叶变换的$q>1$是不可逆的空间密度函数。使用不变性原则，他建造了一个家庭的密度与相同的$q$ -傅立叶变换，并声称$q$ -高斯没有数学证明是吸引子。我们在这里表明，在Hilhorst的反例构造的分布可以是一个极限分布在$q$ -CLT，除了一个支持覆盖整个实轴，这正是$q$ -高斯分布。
英文摘要：
In a recent paper Hilhorst \cite{Hilhorst2010} illustrated that the $q$-Fourier transform for $q>1$ is not invertible in the space of density functions. Using an invariance principle he constructed a family of densities with the same $q$-Fourier transform and claimed that $q$-Gaussians are not mathematically proved to be attractors. We show here that none of the distributions constructed in Hilhorst's counterexamples can be a limit distribution in the $q$-CLT, except the one whose support covers the whole real axis, which is precisely the $q$-Gaussian distribution.
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