On the nature of the Tsallis-Fourier Transform

Abstract

By recourse to tempered ultradistributions, we show here that the effect of a q-Fourier transform (qFT) is to map {\it 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 on individual ones, as orthodox statistics does. We solve here the qFT's non-invertibility issue, but discover a problem that remains open.

19 pages, no figures. Title has changed. Text has changed

References in corpus (4)

• Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma
• Power-Law Distributions for a Trapped Ion Interacting with a Classical Buffer Gas
• Analysis of Self-Organized Criticality in the Olami-Feder-Christensen model and in real earthquakes
• Inversion of Tsallis' q-Fourier Transform and the complex-plane generalization

Cited by in corpus (2)

• The Legendre Transform in Non-additive Thermodynamics and Complexity
• The ${\tau }_q$-Fourier transform: covariance and uniqueness