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On the Nature of the Tsallis–Fourier Transform

La Plata Physics Institute-CCT-Conicet-Exact Sciences Faculty, Universidad Nacional (UNLP), C.C. 727, 1900 La Plata, Argentina
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Academic Editor: Palle E.T. Jorgensen
Mathematics 2015, 3(3), 644-652; https://doi.org/10.3390/math3030644
Received: 2 May 2015 / Revised: 11 July 2015 / Accepted: 13 July 2015 / Published: 21 July 2015
(This article belongs to the Special Issue Mathematical physics)
By recourse to tempered ultradistributions, we show here that the effect of a q-Fourier transform (qFT) is to map equivalence classes of functions into other classes in a one-to-one fashion. This suggests that Tsallis’ q-statistics may revolve around equivalence classes of distributions and not individual ones, as orthodox statistics does. We solve here the qFT’s non-invertibility issue, but discover a problem that remains open. View Full-Text
Keywords: q-Fourier transform; tempered ultradistributions q-Fourier transform; tempered ultradistributions
MDPI and ACS Style

Plastino, A.; Rocca, M.C. On the Nature of the Tsallis–Fourier Transform. Mathematics 2015, 3, 644-652. https://doi.org/10.3390/math3030644

AMA Style

Plastino A, Rocca MC. On the Nature of the Tsallis–Fourier Transform. Mathematics. 2015; 3(3):644-652. https://doi.org/10.3390/math3030644

Chicago/Turabian Style

Plastino, A., and Mario C. Rocca. 2015. "On the Nature of the Tsallis–Fourier Transform" Mathematics 3, no. 3: 644-652. https://doi.org/10.3390/math3030644

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