Functional-differential equations for the q-Fourier transform of q-Gaussians
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چکیده
In the paper the question Is the q-Fourier transform of a qGaussian 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.
منابع مشابه
Functional-differential equations for Fq-transforms of q-Gaussians
In the paper the question is a q-Fourier transform of a q-Gaussian a q ′ -Gaussian (with some q ′ ) up to a constant factor is analyzed for the whole range of q ∈ (−∞, 3). This question is connected with applicability of Fq-transform in the study of limit processes in nonextensive statistical mechanics. We derive some functional-differential equations for the q-Fourier transform of q-Gaussians....
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تاریخ انتشار 2009