Mathematical Analysis
Estimating the first zero of a characteristic function
Comptes Rendus. Mathématique, Volume 338 (2004) no. 3, pp. 203-206.

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.

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.

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Published online:
DOI: 10.1016/j.crma.2003.11.028
Luo, Shunlong 1; Zhang, Zhengmin 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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Luo, Shunlong; Zhang, Zhengmin. 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. http://www.numdam.org/articles/10.1016/j.crma.2003.11.028/

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