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.
q-generalized representation of the d-dimensional Dirac delta and q-Fourier transform / Sicuro G.; Tsallis C.. - In: PHYSICS LETTERS A. - ISSN 0375-9601. - ELETTRONICO. - 381:32(2017), pp. 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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