Probability theory/Harmonic analysis
A theorem of uniqueness for characteristic functions
Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 920-924.

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]R, 0[a,b], there exists a characteristic function f such that fet2/2, but f(t)=et2/2 for all t[a,b]?

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]R, 0[a,b], est-il vrai qu'il existe une fonction caractéristique f telle que fet2/2, mais vérifiant f(t)=et2/2 pour t[a,b] ?

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2017.07.005
Norvidas, Saulius 1

1 Vilnius University Institute of Mathematics and Informatics, Akademijos 4, 08663 Vilnius, Lithuania
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Norvidas, Saulius. 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. http://www.numdam.org/articles/10.1016/j.crma.2017.07.005/

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