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Comptes Rendus Mathématique
Volume 339, n° 5
pages 335-337 (septembre 2004)
Doi : 10.1016/j.crma.2004.07.009
Received : 17 June 2004 ;  accepted : 12 July 2004
The zero-one law for a complete orthonormal system
La loi zéro-un pour un système orthonormal complet.
 

Kazaros Kazarian
Departamento de Matemáticas,C-XV, Universidad Autónoma de Madrid, 28049 Madrid, Spain 

Abstract

A complete orthonormal system of functions   is constructed such that   converges almost everywhere on   if   and   diverges a.e. for any  . We also show that for any complete ONS   of functions defined on   there exists a fixed non decreasing subsequence   of natural numbers such that for any   and some sequence of coefficients  ,
n=1nkbnfnfa.e. whenk. To cite this article: K. Kazarian, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

The full text of this article is available in PDF format.
Résumé

On construit un système orthonormal complet   tel que   converge presque partout pour n'importe quel   et diverge presque partout pour n'importe quel  . Nous démontrons que pour toute système orthonormal complet   il existe une sous suite croissante   d'entiers naturels tels que pour tout   il existe une suite de coefficients tels que
n=1Nkbnfnfp.p. sik. Pour citer cet article : K. Kazarian, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

The full text of this article is available in PDF format.


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