$q$-Generalized representation of the $d$-dimensional Dirac delta and $q$-Fourier transform

Abstract

We discuss a generalized representation of the Dirac delta function in $d$ dimensions in terms of $q$-exponential functions. We apply this new representation to the study of the so-called $q$-Fourier transform, proving its invertibility for any value of $d$. We finally illustrate the effect of the $q$-deformation on the Gibbs phenomenon.

arXiv comment6 pages, 3 figures

References in corpus (16)

• Superstatistics
• The Physics and Mathematics of the Second Law of Thermodynamics
• Transverse-momentum and pseudorapidity distributions of charged hadrons in pp collisions at sqrt(s) = 7 TeV
• Nonextensivity and multifractality in low-dimensional dissipative systems
• Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma
• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• Option Pricing Formulas based on a non-Gaussian Stock Price Model
• Thermostatistics of overdamped motion of interacting particles
• Nonextensive Pesin identity. Exact renormalization group analytical results for the dynamics at the edge of chaos of the logistic map
• Ensemble averages and nonextensivity at the edge of chaos of one-dimensional maps
• Note on a q-modified central limit theorem
• q-Generalization of the inverse Fourier transform
• New representations of pi and Dirac delta using the nonextensive-statistical-mechanics q-exponential function
• Formal Groups and $Z$-Entropies
• On a conjecture about Dirac's delta representation using q-exponentials
• A direct proof of Jauregui-Tsallis' conjecture

Cited by in corpus (2)

• Microscopic Dynamics of Nonlinear Fokker-Planck Equations
• A generalized Vitali set from nonextensive statistics