2017/05/31 by Gabriele Sicuro, Constantino Tsallis · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Dirac (video compression format) #Dirac algebra #Dirac comb #Dirac delta function #Dirac equation #Dirac spinor #Exponential function #Fourier analysis #Fourier series #Fourier transform #Fractional Differential Equations Solutions #Function (biology) #Gibbs phenomenon #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #Representation (politics) #Statistical Mechanics and Entropy #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1016/j.physleta.2017.06.006
published as Phys. Lett. A 381(32), 2583-2587 (2017) · 6 pages, 3 figures
openalex created_date 2017/05/12 · openalex publication_date 2017/06/07 · arxiv created 2017/06/15 · arxiv updated 2017/07/25 · openalex updated_date 2026/08/05
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.