标题： q-矩消除了与q-傅里叶变换反演相关的退化性 显示英文标题

标题： q-Moments remove the degeneracy associated with the inversion of the q-Fourier transform

摘要： 最近在 [Hilhorst, JSTAT, P10023 (2010)] 中证明，对于 q > 1，在概率密度函数的整个空间中，傅里叶变换的 q-广义形式是不可逆的。 最近也已经显示，如果我们不仅对函数本身，而且对其所有位移都放弃 q-傅里叶变换，这种复杂性就会消失 [Jauregui 和 Tsallis, Phys. Lett. A 375, 2085 (2011)]。 在这里，我们表明，对于给定的概率密度函数的 q-傅里叶变换的逆问题，存在另一种完全消除退化的方法。 事实上，如果我们掌握与它的 q-矩相关的额外信息，就可以确定这个密度。 显示英文摘要

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.