Smoothness characterization and stability for nonlinear multiscale representations

The goal of this Note is to present some theoretical results for the nonlinear multiscales representations concerning the smoothness characterization through the rate of decay of multiscales coefficients and stability. We introduce a general framework to analyze such properties. To cite this article: B. Matei, C. R. Acad. Sci. Paris, Ser. I 338 (2004).