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κ-deformed Fourier transform

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  • Scarfone, A.M.

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.

Suggested Citation

  • Scarfone, A.M., 2017. "κ-deformed Fourier transform," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 480(C), pages 63-78.
    • Handle: RePEc:eee:phsmap:v:480:y:2017:i:c:p:63-78
    DOI: 10.1016/j.physa.2017.03.036
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    References listed on IDEAS

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    1. Umarov, Khojamahmad, 2016. "Сельскохозяйственная Политика В Производстве Хлопка И Диверсификация Агропромышленного Комплекса В Таджикистане [Agricultural policy in cotton production and the diversification of the agricultural," IAMO Discussion Papers 159, Leibniz Institute of Agricultural Development in Transition Economies (IAMO).
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    Cited by:

    1. Nakamura, Gilberto M. & de Martini, Alexandre H. & Martinez, Alexandre S., 2019. "Extension of inverse q-Fourier transform via conformal mapping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 106-111.

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