Restricted Nonlinear Approximation Academic Article uri icon


  • We introduce a new form of nonlinear approximation called restricted approximation. It is a generalization of n-term wavelet approximation in which a weight function is used to control the terms in the wavelet expansion of the approximant. This form of approximation occurs in statistical estimation and in the characterization of interpolation spaces for certain pairs of Lp and Besov spaces. We characterize, both in terms of their wavelet coefficients and also in terms of their smoothness, the functions which are approximated with a specified rate by restricted approximation. We also show the relation of this form of approximation with certain types of thresholding of wavelet coefficients.

published proceedings

  • Constructive Approximation

author list (cited authors)

  • Cohen, A., DeVore, R. A., & Hochmuth, R.

citation count

  • 52

complete list of authors

  • Cohen, A||DeVore, RA||Hochmuth, R

publication date

  • January 2000