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Mathematics 2015, 3(3), 644-652;

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
Author to whom correspondence should be addressed.
Academic Editor: Palle E.T. Jorgensen
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)
Full-Text   |   PDF [201 KB, uploaded 21 July 2015]


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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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MDPI and ACS Style

Plastino, A.; Rocca, M.C. On the Nature of the Tsallis–Fourier Transform. Mathematics 2015, 3, 644-652.

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