Restricted nonlinear approximation
This paper introduces 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 \(L_p\) and Besov spaces. This paper characterizes, 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. This paper also shows the relation of this form of approximation with certain types of thresholding of wavelet coefficients.
characterization of approximation classes
scientific article; zbMATH DE number 1419735