Plastino, A.; Rocca, M. C. A direct proof of Jauregui-Tsallis’ conjecture. (English) Zbl 1272.46031 J. Math. Phys. 52, No. 10, 103503, 7 p. (2011). Summary: We give here the direct proof of a recent conjecture of Jauregui and Tsallis about a new representation of Dirac’s delta distribution by means of q-exponentials. The proof is based on the use of tempered ultradistributions’ theory.{©2011 American Institute of Physics} Cited in 2 Documents MSC: 46F05 Topological linear spaces of test functions, distributions and ultradistributions Keywords:Dirac’s delta distribution; tempered ultradistribution theory PDFBibTeX XMLCite \textit{A. Plastino} and \textit{M. C. Rocca}, J. Math. Phys. 52, No. 10, 103503, 7 p. (2011; Zbl 1272.46031) Full Text: DOI arXiv References: [1] Scroeder M., Fractals, Chaos, Power Laws (1991) [2] Gell-Mann M., Nonextensive Entropy: Interdisciplinary Applications (2004) [3] DOI: 10.1590/S0103-97331999000100005 [4] DOI: 10.1590/S0103-97331999000100005 [5] DOI: 10.1590/S0103-97331999000100005 [6] DOI: 10.1016/j.physleta.2007.02.003 · Zbl 1203.82005 [7] DOI: 10.1016/j.physleta.2007.02.003 · Zbl 1203.82005 [8] DOI: 10.1016/j.physleta.2006.07.005 · Zbl 05321985 [9] Goldenfeld N., Lectures on Phase Transitions and the Renormalization Group (1992) · Zbl 0825.76872 [10] Tsallis C., Introduction to Nonextensive Statistical Mechanics (2009) · Zbl 1172.82004 [11] DOI: 10.1016/S0378-4371(03)00019-0 · Zbl 1038.82049 [12] Gell-Mann M., Nonextensive Entropy: Interdisciplinary Applications (2004) · Zbl 0959.82500 [13] DOI: 10.1016/0375-9601(94)90948-2 · Zbl 0959.82500 [14] Kaniadakis G., Physica A (Special) 305 (2002) [15] DOI: 10.1016/0375-9601(94)90592-4 · Zbl 0959.82512 [16] DOI: 10.1063/1.3431981 · Zbl 1311.46039 [17] DOI: 10.1063/1.3478886 · Zbl 1309.46021 [18] Reif F., Statistical and Thermal Physics (1965) [19] Pathria R. K., Statistical Mechanics (1993) [20] Gibbs J. W., Elementary Principles in Statistical Mechanics in Collected Works (1948) · Zbl 0031.13504 [21] Lindsay R. B., Foundations of Physics (1957) [22] L. S. Gradshtein and I. M. Ryzhik,Table of Integrals, Series, and Products, 6th ed. (Academic, New York, 2000), p. 313, 3.194, formula 3. [23] e Silva J. Sebastiao, Math. Ann. 136 pp 38– (1958) [24] DOI: 10.2748/tmj/1178244354 · Zbl 0103.09201 [25] Schwartz L., Théorie des distributions (1966) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.