The standard q-Fourier Transform (qFT) of a constant diverges, which begs for a better treatment. In addition, Hilhorst has conclusively proved that the ordinary qFT is not of a one-to-one character for an infinite set of functions [H.J. Hilhorst, J. Stat. Mech. (2010) P10023]. Generalizing the...

We introduce here the q-Laplace transform as a new weapon in Tsallis’ arsenal, discussing its main properties and analyzing some examples. The q-Gaussian instance receives special consideration. Also, we derive the q-partition function from the q-Laplace transform.

We introduce a complex q-Fourier transform as a generalization of the (real) one analyzed in [S. Umarov, C. Tsallis, S. Steinberg, Milan J. Math. 307 (2008)]. By recourse to tempered ultradistributions we show that this complex-plane generalization overcomes all the troubles that afflict its...