no. 21-22
Mathematical Analysis
Continuous functions with universally divergent Fourier series on small subsets of the circle
[Fonctions continues avec des séries de Fourier universellement divergentes sur des petites parties du cercle]
Présenté par : Jean-Pierre Kahane
Müller, Jürgen1
1 Universität Trier, FB IV, Mathematik, 54286 Trier, Germany
Comptes Rendus. Mathématique, Tome 348 (2010) no. 21-22, pp. 1155-1158

It is shown that quasi all continuous functions on the unit circle have the property that, for many small subsets E of the circle, the partial sums of their Fourier series considered as functions restricted to E exhibit certain universality properties.

Nous démontrons pour quasi toutes les fonctions continues sur le cercle unitaire que, pour de nombreuses petites parties E du cercle, les sommes partielles de leurs séries de Fourier présentent certaines propriétés d'universalité sur E.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.10.026

Müller, Jürgen 1

1 Universität Trier, FB IV, Mathematik, 54286 Trier, Germany 
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Müller, Jürgen. Continuous functions with universally divergent Fourier series on small subsets of the circle. Comptes Rendus. Mathématique, Tome 348 (2010) no. 21-22, pp. 1155-1158. doi: 10.1016/j.crma.2010.10.026

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