Smoothness characterization and stability of nonlinear and non-separable multiscale representations (Q643347)

The analysis of multivariate functions carried out with tensor-product representation is not optimal. This paper is devoted to studying the construction and analysis of nonlinear and non-separable multiscale representations for multivariate functions. Furthermore, this paper characterizes the functions in \(Lp\) and Besov spaces by their multiscale representations and studies the stability and convergence of these multiscale representations. However, most of the theorems in this paper involve multiscale representations which are generated by data dependent subdivision rules.