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 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.

AB - 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.

KW - Mathematics

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

UR - https://www.mendeley.com/catalogue/ab9c7d13-c300-33c7-a014-b1cc6100111b/

U2 - 10.1002/mana.200410500

DO - 10.1002/mana.200410500

M3 - Journal articles

VL - 280

SP - 523

EP - 533

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 1522-2616

IS - 5-6

ER -