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.
Sicuro G., Tsallis C. (2017). q-generalized representation of the d-dimensional Dirac delta and q-Fourier transform. PHYSICS LETTERS A, 381(32), 2583-2587 [10.1016/j.physleta.2017.06.006].
q-generalized representation of the d-dimensional Dirac delta and q-Fourier transform
Sicuro G.;
2017
Abstract
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.File in questo prodotto:
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