$q$-Generalized representation of the $d$-dimensional Dirac delta and $q$-Fourier transform

Abstract

We discuss a generalized representation of the Dirac delta function in $d$ dimensions in terms of $q$-exponential functions. We apply this new representation to the study of the so-called $q$-Fourier transform, proving its invertibility for any value of $d$. We finally illustrate the effect of the $q$-deformation on the Gibbs phenomenon.

6 pages, 3 figures

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• Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma
• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• Thermostatistics of overdamped motion of interacting particles

Cited by in corpus (1)

• Microscopic Dynamics of Nonlinear Fokker-Planck Equations