Bases d'ondelettes adaptées au règlement de la divergence infra-rouge

We propose bi-orthogonal wavelet bases that solve the problem of infrared divergence phenomenon for usual wavelet expansions in the homogeneous Sobolev spaces H˙s(Rn). These bases remove the divergence in the case s−n2∉N since they are also bases of the realization of H˙s(Rn). In the critical case s−n2∈N, they provide a confinement of the infrared divergence in a 'small' space. This method of confinement is also applied to the Mumford process. To cite this article: B. Vedel, C. R. Acad. Sci. Paris, Ser. I 341 (2005).