Smoothness characterization and stability in nonlinear multiscale framework: theoretical results

Article type: Research Article

Authors: Matei, Basarab

Affiliations: Laboratoire Jacques‐Louis Lions, Université Pierre et Marie Curie, 175, rue du Chevaleret, 75013 Paris, France E‐mail: matei@ann.jussieu.fr

Abstract: The aim of this paper is to characterize the smoothness of a function belonging to a Hölder or to a Besov space, by the rate of decay of its nonlinear multiscale coefficients. The study is carried out in the general framework of nonlinear multiscale representations of data due to A. Harten. We also study the stability of these representations, a key issue in their applications to design adaptive algorithms.

Journal: Asymptotic Analysis, vol. 41, no. 3-4, pp. 277-309, 2005