Sur l'équation fonctionnelle ∫T(ψ(t+s)−ψ(s))3ds=sint

Clearly the equation given in the title has no solution in Cα, α>13. We give an explicit solution in C1/3. The motivation for this question, and other questions of the same type, comes from the forthcoming article by H. Brezis. To cite this article: J.-P. Kahane, C. R. Acad. Sci. Paris, Ser. I 341 (2005).