Comptes Rendus
Mathematical Analysis
Continuous functions with universally divergent Fourier series on small subsets of the circle
Comptes Rendus. Mathématique, Volume 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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2010.10.026

Jürgen Müller 1

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

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[5] V. Nestoridis Universal Taylor series, Ann. Inst. Fourier (Grenoble), Volume 46 (1996), pp. 1293-1306

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