Restricted Nonlinear Approximation
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- 作者：A. Cohen ; R. A. DeVore and R. Hochmuth
- 关键词：Key words. Restricted approximation ; Nonlinear approximation ; Characterization of approximation classes ; Besov spaces ; K ; functionals. AMS Classification. 41 ; 41A17 ; 41A25 ; 41A46.
- 刊名：Constructive Approximation
- 出版时间：April 2000
- 出版年：2000
- 期刊代码：34_0176-4276
- 类别：bs
- 卷：16
- 期：1
- 页码：85-113
- 数据来源：sp
摘要
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 L p 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.