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

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We introduce 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 and we establish the analytical procedure through which it can be inverted for any value of d. We finally illustrate the effect of the q-deformation on the Gibbs phenomenon of Fourier series expansions.

G. Sicuro, C. Tsallis, q-generalized representation of the d-dimensional Dirac delta and q-Fourier transform, Physics Letters A, Volume 381, Issue 32 (August 2017) 2559–2658