caa a22 4500 475743598 CHVBK 20180406123506.0 cr unu---uuuuu 170329e20000101xx s 000 0 eng 10.1007/s003659910004 doi (NATIONALLICENCE)springer-10.1007/s003659910004 Restricted Nonlinear Approximation [Elektronische Daten] [A. Cohen, R. A. DeVore, R. Hochmuth] Abstract. : 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. Springer-Verlag New York Inc., 2000 Key words. Restricted approximation, Nonlinear approximation, Characterization of approximation classes, Besov spaces, K -functionals. AMS Classification. 41, 41A17, 41A25, 41A46 nationallicence Cohen A. Laboratoire d'Analyse Numérique Université Pierre et Marie Curie, 75252 Paris cedex 05, France aut DeVore R. A. Department of Mathematics, University of South Carolina, SC 29208, Columbia, USA aut Hochmuth R. I. Mathematisches Institut Freie Universität Berlin, Arnimallee 3, 14195, Berlin, Germany aut https://doi.org/10.1007/s003659910004 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003659910004 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cohen A. Laboratoire d'Analyse Numérique Université Pierre et Marie Curie, 75252 Paris cedex 05, France aut NATIONALLICENCE 700 1- DeVore R. A. Department of Mathematics, University of South Carolina, SC 29208, Columbia, USA aut NATIONALLICENCE 700 1- Hochmuth R. I. Mathematisches Institut Freie Universität Berlin, Arnimallee 3, 14195, Berlin, Germany aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer