Reflections on the q-Fourier transform and the q-Gaussian function

A. Plastino and M.C. Rocca

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 18, 3952-3961

Abstract: 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 ordinary qFT analyzed in [S. Umarov, C. Tsallis, S. Steinberg, Milan J. Math. 76 (2008) 307], we appeal here to a complex q-Fourier transform, and show that the problems above mentioned are overcome.

Keywords: q-Fourier transform; Tempered ultradistributions; Complex-plane generalization; One-to-one character (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:18:p:3952-3961

DOI: 10.1016/j.physa.2013.04.047

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