Restricted nonlinear approximation

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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.
Original languageEnglish
JournalConstructive Approximation
Issue number1
Pages (from-to)85-113
Number of pages29
Publication statusPublished - 01.01.2000
Externally publishedYes

    Research areas

  • Mathematics - Besov spaces, Characterization of approximation classes, K -functional, Nonlinear approximation, Restricted approximation, AMS Classification. 41, 41A17, 41A25, 41A46.