Harmonic Analysis/Mathematical Analysis
A null series with small anti-analytic part

Presented by: Jean-Pierre Kahane

Kozma, Gady1; Olevskiǐ, Alexander2
1 The Weizmann Institute of Science, Rehovot, Israel
2 School of Mathematical Sciences, Tel Aviv University, Ramat Aviv 69978, Israel
Comptes Rendus. Mathématique, Volume 336 (2003) no. 6, pp. 475-478.

We show that it is possible for an L2 function on the circle, which is a sum of an almost everywhere convergent series of exponentials with positive frequencies, to not belong to the Hardy space H2. A consequence in the uniqueness theory is obtained.

Il existe une série trigonométrique dont toutes les fréquences sont positives et qui converge presque partout vers une fonction de carré intégrable qui admet des fréquences négatives. Ce fait est équivalent à l'existence de la série trigonométrique mentionnée dans le titre. Il s'agit donc d'une contribution à la théorie de l'unicité du développement trigonométrique.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(03)00097-9
Kozma, Gady 1; Olevskiǐ, Alexander 2

1 The Weizmann Institute of Science, Rehovot, Israel
2 School of Mathematical Sciences, Tel Aviv University, Ramat Aviv 69978, Israel 
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Kozma, Gady; Olevskiǐ, Alexander. A null series with small anti-analytic part. Comptes Rendus. Mathématique, Volume 336 (2003) no. 6, pp. 475-478. doi : 10.1016/S1631-073X(03)00097-9. https://www.numdam.org/articles/10.1016/S1631-073X(03)00097-9/

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