q-矩消除了与q-傅立叶变换的逆相关联的退化
q-Moments remove the degeneracy associated with the inversion of the q-Fourier transform
摘要：
最近证明[Hilhorst，JSTAT，P10023（2010）]，傅立叶变换的q-推广在q > 1的概率密度函数的全空间中是不可逆的。最近还表明，如果我们不仅处理函数本身的q-傅立叶变换，而且处理其所有移位，则这种复杂性消失[Jauregui和Tsallis，Phys. Lett. A 375，2085（2011）]。在这里，我们表明，另一条道路存在完全消除退化与给定的概率密度函数的q-傅立叶变换的逆。事实上，如果我们处理一些与它的q矩有关的额外信息，就有可能确定这个密度。
英文摘要：
It was recently proven [Hilhorst, JSTAT, P10023 (2010)] that the q-generalization of the Fourier transform is not invertible in the full space of probability density functions for q > 1. It has also been recently shown that this complication disappears if we dispose of the q-Fourier transform not only of the function itself, but also of all of its shifts [Jauregui and Tsallis, Phys. Lett. A 375, 2085 (2011)]. Here we show that another road exists for completely removing the degeneracy associated with the inversion of the q-Fourier transform of a given probability density function. Indeed, it is possible to determine this density if we dispose of some extra information related to its q-moments.
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