Full length article: Smoothness characterization and stability of nonlinear and non-separable multiscale representations

Authors:
Basarab Matei;Sylvain Meignen;Anastasia Zakharova
Affiliations:
LAGA Laboratory, Paris XIII University, France;LJK Laboratory, University of Grenoble, France;LJK Laboratory, University of Grenoble, France
Venue:
Journal of Approximation Theory
Year:
2011

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Abstract

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 M. We show that a function in L^p 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.