q-Fourier Transform and its inversion-problem
A. Plastino, M.C.Rocca
TL;DR
This paper addresses the non-invertibility of Tsallis' q-Fourier transform by proposing a generalized extension that allows the parameter q to vary, restoring its one-to-one property.
Contribution
The paper introduces a simple extension of the q-Fourier transform that allows q to vary, resolving the invertibility issue present in the original formulation.
Findings
The extended q-Fourier transform is one-to-one when q is allowed to vary.
The modification preserves the transform's usefulness while fixing its mathematical limitations.
The approach simplifies the inversion process of the q-Fourier transform.
Abstract
Tsallis' q-Fourier transform is not generally one-to-one. It is shown here that, if we eliminate the requirement that be fixed, and let it instead "float", a simple extension of the definition, this procedure restores the one-to-one character.
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Taxonomy
TopicsStatistical Mechanics and Entropy · Fractional Differential Equations Solutions · Advanced Statistical Methods and Models