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 . 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.
Cite
@article{arxiv.0802.0264,
title = {Functional-differential equations for $F_q$%-transforms of $q$-Gaussians},
author = {Sabir Umarov and Silvio M. Duarte Queiros},
journal= {arXiv preprint arXiv:0802.0264},
year = {2010}
}
Comments
14 pages A new section on a related solution of the porous medium equation in comparison with the previous version has been introduce