Inégalités d'incertitude associées à des fonctions homogènes

The uncertainty principle states that a nonzero function and its Fourier transform cannot be both sharply localized. It is well known that the support and the spectrum of a function cannot both have finite measure. In Shubin et al. [Geom. Funct. Anal. 8 (1998) 932-964], it is shown that they cannot be contained in ɛ-thin sets E and Eˆ. We give here other examples of sets E and Eˆ having this property. The thinness of the sets is expressed in terms of a dyadic decomposition of the space, which is related to the functions |x1|α1⋯|xd|αd on Rd. These sets are not ɛ-thin in general. We prove that the pairs of sets we consider are strongly annihilating in the sense of Havin and Jöricke. To cite this article: B. Demange, C. R. Acad. Sci. Paris, Ser. I 340 (2005).