On a representation of the inverse Fq-transform

A generalization of the Central Limit Theorem consistent with nonextensive statistical mechanics has been recently achieved through a generalized Fourier transform, noted q-Fourier transform. A representation formula for the inverse q-Fourier transform is here obtained in the class of functions G=⋃1⩽q 0,β>0}. This constitutes a first step towards a general representation of the inverse q-Fourier operation, which would enable interesting physical and other applications.