On a representation of the inverse Fq transform

Abstract

A recent 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 $\mathcal{G}={\bigcup }_{1\le q<3}{\mathcal{G}}_q,$ where ${\mathcal{G}}_q=\{f=a{e}_q^{-\beta x2},a>0,\beta >0\}$. This constitutes a first step towards a general representation of the inverse $q$-Fourier operation, which would enable interesting physical and other applications.

4 pages

References in corpus (2)

• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• A generalization of the central limit theorem consistent with nonextensive statistical mechanics

Cited by in corpus (2)

• On the role of ergodicity and mixing in the central limit theorem for Casati-Prosen triangle map variables
• The Relationship between Tsallis Statistics, the Fourier Transform, and Nonlinear Coupling