Functional-differential equations for $F_q$%-transforms of $q$-Gaussians

Abstract

In the paper the question - Is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor? - is studied for the whole range of $q\in (-\infty ,3)$. This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. We prove that the answer is affirmative if and only if q > 1, excluding two particular cases of q<1, namely, q = 1/2 and q = 2/3, which are also out of the theory valid for q \ge 1. We also discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.

14 pages A new section on a related solution of the porous medium equation in comparison with the previous version has been introduce

References in corpus (5)

• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• Option Pricing Formulas based on a non-Gaussian Stock Price Model
• Generalized algebra within a nonextensive statistics
• Numerical indications of a q-generalised central limit theorem
• On a representation of the inverse Fq transform

Cited by in corpus (6)

• Note on a q-modified central limit theorem
• Entropic Forms and Related Algebras
• On q-Gaussians and Exchangeability
• The limit distribution in the $q$-CLT for $q\ge 1$ is unique and can not have a compact support
• Reflections on the q-Fourier transform and the q-Gaussian function
• One and two side generalisations of the log-Normal distribution by means of a new product definition