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 ...

By recourse to tempered ultradistributions, we show here that the effect of a q-Fourier transform (qFT) is to map equivalence classes of functions into other classes in a one-to-one fashion. This suggests that Tsallis’ ...

Tsallis' q-Fourier transform is not generally one-to-one. It is shown here that, if we eliminate the requirement that q be fixed, and let it instead "float", a simple extension of the F q definition, this procedure restores ...

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 ...

We introduce an explicit representation of the double affine Hecke algebra (of type A(1)) at q = 1 that gives rise to a periodic counterpart of a well-known Fourier transform associated with the affine Hecke algebra. (C) ...