$q$-Generalized representation of the $d$-dimensional Dirac delta and $q$-Fourier transform
arXiv:1705.01584 · doi:10.1016/j.physleta.2017.06.006
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