Inversion of Tsallis' q-Fourier Transform and the complex-plane generalization
A. Plastino, M.C.Rocca
TL;DR
This paper introduces a complex q-Fourier transform using tempered ultradistributions, overcoming issues present in the real version and generalizing the transform to the complex plane.
Contribution
The paper presents a novel complex-plane generalization of the q-Fourier transform utilizing tempered ultradistributions, addressing previous limitations.
Findings
Overcomes limitations of the real q-Fourier transform
Uses tempered ultradistributions for the generalization
Provides a mathematically rigorous complex-plane extension
Abstract
We introduce a complex q-Fourier transform as a generalization of the (real) one analyzed in [Milan J. Math. {\bf 76} (2008) 307]. By recourse to tempered ultradistributions we show that this complex plane-generalization overcomes all troubles that afflict its real counterpart.
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