A theorem of uniqueness for characteristic functions

Saulius Norvidas

doi:10.1016/j.crma.2017.07.005

Probability theory/Harmonic analysis

A theorem of uniqueness for characteristic functions
[Théorème d'unicité pour les fonctions caractéristiques]

Présenté par : the Editorial Board

Saulius Norvidas ¹

¹ Vilnius University Institute of Mathematics and Informatics, Akademijos 4, 08663 Vilnius, Lithuania

Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 920-924.

Résumé
Abstract

Nous discutons d'une propriété d'unicité pour : les fonctions caractéristiques des mesures de probabilité. Notre étude tire son origine dans la question de N.G. Ushakov : étant donné $[a, b] \subset R$ , $0 \notin [a, b]$ , est-il vrai qu'il existe une fonction caractéristique f telle que $f ≢ e^{- t^{2} / 2}$ , mais vérifiant $f (t) = e^{- t^{2} / 2}$ pour $t \in [a, b]$ ?

We discuss a uniqueness property of the characteristic function of an absolutely continuous probability measure. Our study is initiated by the question posed by N.G. Ushakov: is it true that, for any interval $[a, b] \subset R$ , $0 \notin [a, b]$ , there exists a characteristic function f such that $f ≢ e^{- t^{2} / 2}$ , but $f (t) = e^{- t^{2} / 2}$ for all $t \in [a, b]$ ?

Reçu le : 2017-04-22
Accepté le : 2017-07-11
Publié le : 2017-07-27

DOI : 10.1016/j.crma.2017.07.005

Affiliations des auteurs :

Saulius Norvidas ¹

¹ Vilnius University Institute of Mathematics and Informatics, Akademijos 4, 08663 Vilnius, Lithuania

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     author = {Saulius Norvidas},
     title = {A theorem of uniqueness for characteristic functions},
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     volume = {355},
     number = {8},
     year = {2017},
     doi = {10.1016/j.crma.2017.07.005},
     language = {en},
}

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Saulius Norvidas. A theorem of uniqueness for characteristic functions. Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 920-924. doi : 10.1016/j.crma.2017.07.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.07.005/

Bibliographie
Cité par

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[6] S. Norvidas On extensions of characteristic functions, Lith. Math. J., Volume 57 (2017) no. 2, pp. 236-243

[7] N.G. Ushakov Selected Topics in Characteristic Functions, VSP, Utrecht, The Netherlands, 1999

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