Mathematical Analysis
A complete orthonormal system of divergence
[Un système orthonormal complet de divergence]
Comptes Rendus. Mathématique, Tome 337 (2003) no. 2, pp. 85-88.

On construit un système complet orthonormal {Θ n } n=1 ,Θ n L [0,1] tel que ∑n=1anΘn diverge presque partout pour n'importe quel {an}n=1l2. Pour le système construit le résultat suivant est vrai : Toute série suivant le système {Θn}n=1 non triviale et qui converge en mesure vers zéro diverge presque partout.

A complete orthonormal system of functions {Θ n } n=1 ,Θ n L [0,1] defined on the closed interval [0,1] is constructed such that ∑n=1anΘn diverges almost everywhere for any {an}n=1l2. For the constructed system the following result is true: Any nontrivial series by the system {Θn}n=1 which converges in measure to zero diverges almost everywhere.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00286-3
Kazarian, Kazaros 1

1 Departamento de Matemáticas,C-XV, Universidad Autónoma de Madrid, 28049 Madrid, Spain
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Kazarian, Kazaros. A complete orthonormal system of divergence. Comptes Rendus. Mathématique, Tome 337 (2003) no. 2, pp. 85-88. doi : 10.1016/S1631-073X(03)00286-3. http://archive.numdam.org/articles/10.1016/S1631-073X(03)00286-3/

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