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.
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