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]

摘要

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.