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On the Nature of the Tsallis–Fourier Transform

Author

Listed:
  • 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)

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.

Suggested Citation

  • A. Plastino & Mario C. Rocca, 2015. "On the Nature of the Tsallis–Fourier Transform," Mathematics, MDPI, vol. 3(3), pages 1-9, July.
    • Handle: RePEc:gam:jmathe:v:3:y:2015:i:3:p:644-652:d:52932
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    References listed on IDEAS

    as
    1. Capurro, A. & Diambra, L. & Lorenzo, D. & Macadar, O. & Martin, M.T. & Mostaccio, C. & Plastino, A. & Rofman, E. & Torres, M.E. & Velluti, J., 1998. "Tsallis entropy and cortical dynamics: the analysis of EEG signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 257(1), pages 149-155.
    2. Lisa Borland, 2002. "Option Pricing Formulas based on a non-Gaussian Stock Price Model," Papers cond-mat/0204331, arXiv.org, revised Sep 2002.
    3. Martin, M.T. & Plastino, A.R. & Plastino, A., 2000. "Tsallis-like information measures and the analysis of complex signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 275(1), pages 262-271.
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