On the Nature of the Tsallis–Fourier Transform

A. Plastino and Mario C. Rocca
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A. Plastino: La Plata Physics Institute-CCT-Conicet-Exact Sciences Faculty, Universidad Nacional (UNLP), C.C. 727, 1900 La Plata, Argentina
Mario C. Rocca: La Plata Physics Institute-CCT-Conicet-Exact Sciences Faculty, Universidad Nacional (UNLP), C.C. 727, 1900 La Plata, Argentina

Mathematics, 2015, vol. 3, issue 3, 1-9

Abstract: 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.

Keywords: q-Fourier transform; tempered ultradistributions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2015
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