Régularité maximale de la partie anti-analytique d'une série trigonométrique nulle presque partout

Translated title of the contribution: Maximal smoothness of the anti-analytic part of a trigonometric null series

Research output: Contribution to journalArticlepeer-review

Abstract

We proved recently (C. R. Acad. Sci. Paris, Ser. I 336 (2003) 475-478) that the anti-analytic part of a trigonometric series, converging to zero almost everywhere, may belong to L2 on the circle. Here we prove that it can even be C, and we characterize precisely the possible degree of smoothness in terms of the rate of decrease of the Fourier coefficients. This sharp condition might be viewed as a 'new quasi-analyticity'.

Translated title of the contributionMaximal smoothness of the anti-analytic part of a trigonometric null series
Original languageFrench
Pages (from-to)515-520
Number of pages6
JournalComptes Rendus Mathematique
Volume338
Issue number7
DOIs
StatePublished - 1 Apr 2004

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