Comptes Rendus
no. 3
Mathematical Analysis
Estimating the first zero of a characteristic function
[Estimation du premier zero d'une fonction caractéristique]

Présenté par : Paul Malliavin

Shunlong Luo1 ; Zhengmin Zhang2
1 Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080 Beijing, PR China
2 School of Mathematics and Statistics, Carleton University, Ottawa, ON K1S 5B6, Canada
Comptes Rendus. Mathématique, Volume 338 (2004) no. 3, pp. 203-206.

Pour une fonction caractéristique (la transformation de Fourier d'une mesure de probabilité), le premier zéro contient des informations importantes. Nous allons présenter une formule générale pour l'estimée inférieure du premier zéro en terme de moments de tout ordre. Le résultat obtenu illustre l'aspect de complémentarité entre le premier zéro et les moments et sera utilisé pour étudier le principe d'incertitude en mécanique quantique.

For a characteristic function (Fourier transform of a probability distribution), the first zero encodes important information. We present a general lower bound estimation of the first zero in terms of a moment of any order. The result proves the complementary nature between the first zero and moments, and has interesting implications for quantum mechanical uncertainty relations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2003.11.028

Shunlong Luo 1 ; Zhengmin Zhang 2

1 Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080 Beijing, PR China
2 School of Mathematics and Statistics, Carleton University, Ottawa, ON K1S 5B6, Canada 
@article{CRMATH_2004__338_3_203_0,
     author = {Shunlong Luo and Zhengmin Zhang},
     title = {Estimating the first zero of a characteristic function},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {203--206},
     publisher = {Elsevier},
     volume = {338},
     number = {3},
     year = {2004},
     doi = {10.1016/j.crma.2003.11.028},
     language = {en},
}
TY  - JOUR
AU  - Shunlong Luo
AU  - Zhengmin Zhang
TI  - Estimating the first zero of a characteristic function
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 203
EP  - 206
VL  - 338
IS  - 3
PB  - Elsevier
DO  - 10.1016/j.crma.2003.11.028
LA  - en
ID  - CRMATH_2004__338_3_203_0
ER  - 
%0 Journal Article
%A Shunlong Luo
%A Zhengmin Zhang
%T Estimating the first zero of a characteristic function
%J Comptes Rendus. Mathématique
%D 2004
%P 203-206
%V 338
%N 3
%I Elsevier
%R 10.1016/j.crma.2003.11.028
%G en
%F CRMATH_2004__338_3_203_0
Shunlong Luo; Zhengmin Zhang. Estimating the first zero of a characteristic function. Comptes Rendus. Mathématique, Volume 338 (2004) no. 3, pp. 203-206. doi : 10.1016/j.crma.2003.11.028. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.11.028/

[1] P.A.M. Dirac The principles of Quantum Mechanics, Clarendon Press, Oxford, 1958

[2] E.A. Gislason; N.H. Sabelli; J.W. Wood New form of the time-energy uncertainty relation, Phys. Rev. A, Volume 31 (1985), pp. 2078-2081

[3] G.H. Holland; A. Sitaram The uncertainty principle: a mathematical survey, J. Fourier Anal. Appl., Volume 3 (1997), pp. 207-236

[4] E. Laeng; C. Morpurgo An uncertainty inequality involving L1-norm, Proc. Amer. Math. Soc., Volume 127 (1999), pp. 3565-3572

[5] S. Lloyd Ultimate physical limits to computation, Nature, Volume 406 (2000), pp. 1047-1053

[6] S.L. Luo; Z. Wang; Q. Zhang An inequality for characteristic functions and its applications to uncertainty relations and quantum Zeno effect, J. Phys. A, Volume 35 (2002), pp. 5935-5941

[7] N. Margolus; L.B. Levitin The maximum speed of dynamical evolution, Physica D, Volume 120 (1998), pp. 188-195

  • Xiongzhi Chen Uniformly consistently estimating the proportion of false null hypotheses via Lebesgue–Stieltjes integral equations, Journal of Multivariate Analysis, Volume 173 (2019), p. 724 | DOI:10.1016/j.jmva.2019.06.003
  • Lin Zhang; Yuan Sun; Shunlong Luo Quantum speed limit for qubit systems: Exact results, Physics Letters A, Volume 382 (2018) no. 37, p. 2599 | DOI:10.1016/j.physleta.2018.07.030
  • Zhen-Yu Xu; Shunlong Luo; W. L. Yang; Chen Liu; Shiqun Zhu Quantum speedup in a memory environment, Physical Review A, Volume 89 (2014) no. 1 | DOI:10.1103/physreva.89.012307
  • Z. Zhang Bounds for Characteristic Functions and Laplace Transforms of Probability Distributions, Theory of Probability Its Applications, Volume 56 (2012) no. 2, p. 350 | DOI:10.1137/s0040585x97985479
  • Ц Цзан; Z Zhang Bounds for characteristic functions and Laplace transforms of probability distributions, Теория вероятностей и ее применения, Volume 56 (2011) no. 2, p. 407 | DOI:10.4213/tvp4385
  • Fu Shuang-Shuang; Li Nan; Luo Shun-Long A Note on Fundamental Limit of Quantum Dynamics Rate, Communications in Theoretical Physics, Volume 54 (2010) no. 4, p. 661 | DOI:10.1088/0253-6102/54/4/15
  • Ulvi Yurtsever Fundamental limits on the speed of evolution of quantum states, Physica Scripta, Volume 82 (2010) no. 3, p. 035008 | DOI:10.1088/0031-8949/82/03/035008
  • B.L.S. Prakasa Rao Inequalities for characteristic functions of multidimensional distributions, Journal of Mathematical Analysis and Applications, Volume 343 (2008) no. 1, p. 22 | DOI:10.1016/j.jmaa.2008.01.032
  • Zhengmin Zhang An upper bound for characteristic functions of lattice distributions with applications to survival probabilities of quantum states, Journal of Physics A: Mathematical and Theoretical, Volume 40 (2007) no. 1, p. 131 | DOI:10.1088/1751-8113/40/1/007
  • Shunlong Luo; Zhengmin Zhang On Decaying Rate of Quantum States, Letters in Mathematical Physics, Volume 71 (2005) no. 1, p. 1 | DOI:10.1007/s11005-004-5095-4

Cité par 10 documents. Sources : Crossref

Commentaires - Politique