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Comptes Rendus Mathématique
Volume 334, n° 4
pages 279-282 (2002)
Doi : S1631-073X(02)02205-7
Received : 5 November 2001 ;  accepted : 13 November 2001
On the “prediction” problem
Sur le problème de prédiction

Alexander Olevskii 1
School of Mathematical Sciences, Tel Aviv University, Ramat Aviv 69978, Israel 

Note presented by Jean-Pierre Kahane


We prove that almost every (in the Baire category sense) weight w on a circle T satisfies the following property: any function from L2(w,T) can be decomposed as a series ∑nZ+c(n)eint which converges in the norm.

We discuss this result in the context of the classical Szegö-Kolmogorov “prediction” theorem. To cite this article: A. Olveskii, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 279-282.

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

Au sens des catégories de Baire, presque tout poids w vérifie la propriété suivante : toute fonction appartenant à L2(w,T) est décomposable en série ∑nZ+c(n)eint convergente en norme. Nous discutons la relation de ce résultat avec le théorème de « prédiction » classique de Szegö-Kolmogorov. Pour citer cet article : A. Olveskii, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 279-282.

The full text of this article is available in PDF format.
1  Research supported in part by the Israel Science Foundation.

© 2002  Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. All Rights Reserved.
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