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 
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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

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