Inversion of Tsallis' q-Fourier Transform and the complex-plane generalization

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.

23 pages, no figures

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