Comptes Rendus
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

Jürgen Müller1
1 Universität Trier, FB IV, Mathematik, 54286 Trier, Germany
Comptes Rendus. Mathématique, Volume 348 (2010) no. 21-22, pp. 1155-1158.

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.

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.

Reçu le :
Accepté le :
Publié le :
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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[2] J.P. Kahane Baire's category theorem and trigonometric series, J. Anal. Math., Volume 80 (2000), pp. 143-182

[3] Y. Katznelson An Introduction to Harmonic Analysis, Cambridge University Press, 2004

[4] T.W. Körner Kahane's Helson curve, Orsay, 1993 (J. Fourier Anal. Appl.) (1995), pp. 325-346 (Special Issue)

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

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