κ-deformed Fourier transform

A.M. Scarfone

Physica A: Statistical Mechanics and its Applications, 2017, vol. 480, issue C, 63-78

Abstract: We present a new formulation of Fourier transform in the picture of the κ-algebra derived in the framework of the κ-generalized statistical mechanics. The κ-Fourier transform is obtained from a κ-Fourier series recently introduced by Scarfone (2013). The kernel of this transform, that reduces to the usual exponential phase in the κ→0 limit, is composed by a κ-deformed phase and a damping factor that gives a wavelet-like behaviour. We show that the κ-Fourier transform is isomorph to the standard Fourier transform through a changing of time and frequency variables. Nevertheless, the new formalism is useful to study, according to Fourier analysis, those functions defined in the realm of the κ-algebra. As a relevant application, we discuss the central limit theorem for the κ-sum of n-iterate statistically independent random variables.

Keywords: Fourier integral transform; Log-periodic oscillations; κ-deformed algebra; Power-law distribution (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:480:y:2017:i:c:p:63-78

DOI: 10.1016/j.physa.2017.03.036

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