q-Generalization of the inverse Fourier transform

Details q-Generalization of the inverse Fourier transform q-Generalization of the inverse Fourier transform

2010-10-29

arxiv.org/abs/1010.6275v3

Phys. Lett. A 375 (2011) 2085--2088

Physics

Mathematical Physics

6 pages, 3 figures. To appear in Physics Letters A

Scientific paper

10.1016/j.physleta.2011.04.014

A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a Central Limit Theorem generalized in the presence of specific correlations between the relevant random variables. In the realm of this theorem, a q-generalized Fourier transform plays an important role. We introduce here a method which univocally determines a distribution from the knowledge of its q-Fourier transform and some supplementary information. This procedure involves a recently q-generalized Dirac delta and the class of functions on which it acts. The present method conveniently extends the inverse of the standard Fourier transform, and is therefore expected to be very useful in the study of many complex systems.

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