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

Gabriele Sicuro; Constantino Tsallis

doi:10.1016/j.physleta.2017.06.006

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

Mathematical Physics 2017-07-25 v2 Statistical Mechanics math.MP

Authors: 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.

Keywords

q-exponential functions Dirac delta function q-Fourier transform q-deformation Gibbs phenomenon generalized representation invertibility

Cite

@article{arxiv.1705.01584,
  title  = {$q$-Generalized representation of the $d$-dimensional Dirac delta and $q$-Fourier transform},
  author = {Gabriele Sicuro and Constantino Tsallis},
  journal= {arXiv preprint arXiv:1705.01584},
  year   = {2017}
}

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6 pages, 3 figures

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

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Keywords

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