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arXiv · 1705.01584

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

Gabriele Sicuro·Constantino Tsallis
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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.

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Gabriele Sicuro, Constantino Tsallis. 2017-06-15. $q$-Generalized representation of the $d$-dimensional Dirac delta and $q$-Fourier transform. https://doi.org/10.1016/j.physleta.2017.06.006

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