Reflections on the q-Fourier transform and the q-Gaussian function

Abstract

We appeal to a complex q-Fourier transform as a generalization of the (real) one analyzed in [Milan J. Math. {\bf 76} (2008) 307]. By recourse to tempered ultra-distributions we are able to show that the q-Gaussian distribution can be nicely obtained, overcoming all troubles that afflict its real counterpart.

28 pages, no figures. Title has changed. Text has changed

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Cited by in corpus (4)

• New Solution of Diffusion-Advection Equation for Cosmic-Ray Transport Using Ultradistributions
• The Legendre Transform in Non-additive Thermodynamics and Complexity
• Some properties of q-Gaussian distributions
• The ${\tau }_q$-Fourier transform: covariance and uniqueness