Reflections on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>q</mml:mi></mml:math>-Fourier transform and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" display="inline" overflow="scroll"><mml:mi>q</mml:mi></mml:math>-Gaussian function

Plastino, A.; Rocca, Mario Carlos

doi:10.1016/j.physa.2013.04.047

Physica A: Statistical Mechanics and its Applications

2013

DOI: 10.1016/j.physa.2013.04.047

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

A. Plastino¹,

Mario Carlos Rocca²

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 1we appeal here to a complex q-Fourier transform, and show that the problems above mentioned are overcome.

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Cited by 5 publications

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In this paper we exactly solve the diffusion-advection equation for cosmic-ray transport. With this purpose we use the Theory of Ultradistributions of J. Sebastiao e Silva, to give a general solution for this equation. From this solution, we obtain several approximations as limiting cases of various situations of physical and astrophysical interest. One of them involves Solar cosmic-rays' diffusion.

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We briefly review the foundations and applications of statistical mechanics based on the nonadditive entropies S q. Then we address four frequently focused points, namely (i) On the form of the constraints within a variational entropy principle; (ii) Are the q-indices first-principle-computable quantities or fitting parameters?; (iii) If one admits violation of the entropic additivity, why not admitting also violation of the entropic extensivity?; and (iv) Critical-like behavior.

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

Cited by 5 publications

References 41 publications

New Solution of Diffusion–Advection Equation for Cosmic-Ray Transport Using Ultradistributions

New Solution of Diffusion–Advection Equation for Cosmic-Ray Transport Using Ultradistributions

The confidence interval of q-Gaussian distributions

On the foundations of statistical mechanics

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