Journal article
Anisotropic wavelet bases and thresholding
Publication Details
Authors: | Hochmuth, R. |
Publication year: | 2007 |
Journal: | Mathematical News |
Pages range : | 523-533 |
Volume number: | 280 |
Start page: | 523 |
End page: | 533 |
ISSN: | 0025-584X |
Abstract
We consider thresholding with respect to anisotropic wavelet bases measuring the approximation error in anisotropic Hardy spaces H-p(a) for p > 0, which are known to be equal to L-p for p > 1. In particular, we characterize those functions that provide a specific convergence rate by intrinsic smoothness properties. To this end we apply restricted nonlinear approximation, see [3], which is a generalization of n-term approximation in which a weight function is used to control the terms of the approximations. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
We consider thresholding with respect to anisotropic wavelet bases measuring the approximation error in anisotropic Hardy spaces H-p(a) for p > 0, which are known to be equal to L-p for p > 1. In particular, we characterize those functions that provide a specific convergence rate by intrinsic smoothness properties. To this end we apply restricted nonlinear approximation, see [3], which is a generalization of n-term approximation in which a weight function is used to control the terms of the approximations. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
