Abstract
In this 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 ∊ (− ∊fty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 ⩽ q < 3, excluding two particular cases of q < 1, namely and Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.
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