Functional-differential equations for Fq%-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∈ (-∞, 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 1. We also discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.
0