Smoothness characterization and stability of nonlinear and non-separable multiscale representations

The aim of the paper is the construction and the analysis of nonlinear and non-separable multiscale representations for multivariate functions defined using a non-diagonal dilation matrix MM. We show that a function in LpLp or Besov spaces can be characterized by means of its multiscale representation. We also study the stability of these representations, a key issue to design adaptive algorithms.