Inversion of Tsallis' q-Fourier Transform and the complex-plane   generalization
  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. 
A. Plastino and M.C.Rocca
math-ph cond-mat.stat-mech math.MP quant-ph