Details
| Original language | English |
|---|---|
| Pages (from-to) | 523-533 |
| Number of pages | 11 |
| Journal | Mathematische Nachrichten |
| Volume | 280 |
| Issue number | 5-6 |
| Publication status | Published - 2007 |
| Externally published | Yes |
Abstract
We consider thresholding with respect to anisotropic wavelet bases measuring the approximation error in anisotropic Hardy spaces Hp a for p > 0, which are known to be equal to Lp 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.
Keywords
- Anisotropic besov spaces, Anisotropic Hardy spaces, Anisotropic wavelet bases, Nonlinear approximation, Restricted nonlinear approximation, Thresholding, Wavelet shrinkage
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Mathematische Nachrichten, Vol. 280, No. 5-6, 2007, p. 523-533.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Anisotropic wavelet bases and thresholding
AU - Hochmuth, Reinhard
PY - 2007
Y1 - 2007
N2 - We consider thresholding with respect to anisotropic wavelet bases measuring the approximation error in anisotropic Hardy spaces Hp a for p > 0, which are known to be equal to Lp 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.
AB - We consider thresholding with respect to anisotropic wavelet bases measuring the approximation error in anisotropic Hardy spaces Hp a for p > 0, which are known to be equal to Lp 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.
KW - Anisotropic besov spaces
KW - Anisotropic Hardy spaces
KW - Anisotropic wavelet bases
KW - Nonlinear approximation
KW - Restricted nonlinear approximation
KW - Thresholding
KW - Wavelet shrinkage
UR - http://www.scopus.com/inward/record.url?scp=34247219773&partnerID=8YFLogxK
U2 - 10.1002/mana.200410500
DO - 10.1002/mana.200410500
M3 - Article
AN - SCOPUS:34247219773
VL - 280
SP - 523
EP - 533
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 0025-584X
IS - 5-6
ER -