On the “prediction” problem
Comptes Rendus. Mathématique, Volume 334 (2002) no. 4, pp. 279-282.

We prove that almost every (in the Baire category sense) weight w on a circle 𝕋 satisfies the following property: any function from L 2 (w,𝕋) can be decomposed as a series

n + c(n)e int
which converges in the norm.

We discuss this result in the context of the classical Szegö–Kolmogorov “prediction” theorem.

Au sens des catégories de Baire, presque tout poids w vérifie la propriété suivante : toute fonction appartenant à L 2 (w,𝕋) est décomposable en série

n + c(n)e int
convergente en norme. Nous discutons la relation de ce résultat avec le théorème de « prédiction » classique de Szegö–Kolmogorov.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(02)02205-7
Olevskii, Alexander 1

1 School of Mathematical Sciences, Tel Aviv University, Ramat Aviv 69978, Israel
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Olevskii, Alexander. On the “prediction” problem. Comptes Rendus. Mathématique, Volume 334 (2002) no. 4, pp. 279-282. doi : 10.1016/S1631-073X(02)02205-7. http://www.numdam.org/articles/10.1016/S1631-073X(02)02205-7/

[1] Koosis, P. Introduction to Hp Spaces, Cambridge University Press, 1980

[2] Kozma, G.; Olevskii, A. Menshov representation spectra, J. Analyse Math., Volume 84 (2001), pp. 361-393

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