N-term approximation in anisotropic function spaces
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In: Mathematische Nachrichten, Vol. 244, No. 1, 2002, p. 131-149.
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TY - JOUR
T1 - N-term approximation in anisotropic function spaces
AU - Hochmuth, Reinhard
PY - 2002
Y1 - 2002
N2 - In L 2((0, 1) 2) infinitely many different biorthogonal wavelet bases may be introduced by taking tensor products of one-dimensional biorthogonal wavelet bases on the interval (0, 1). Most well-known are the standard tensor product bases and the hyperbolic bases. In [23, 24] further biorthogonal wavelet bases are introduced, which provide wavelet characterizations for functions in anisotropic Besov spaces. Here we address the following question: Which of those biorthogonal tensor product wavelet bases is the most appropriate one for approximating nonlinearly functions from anisotropic Besov spaces? It turns out, that the hyperbolic bases lead to nonlinear algorithms which converge as fast as the corresponding schemes with respect to specific anisotropy adapted bases.
AB - In L 2((0, 1) 2) infinitely many different biorthogonal wavelet bases may be introduced by taking tensor products of one-dimensional biorthogonal wavelet bases on the interval (0, 1). Most well-known are the standard tensor product bases and the hyperbolic bases. In [23, 24] further biorthogonal wavelet bases are introduced, which provide wavelet characterizations for functions in anisotropic Besov spaces. Here we address the following question: Which of those biorthogonal tensor product wavelet bases is the most appropriate one for approximating nonlinearly functions from anisotropic Besov spaces? It turns out, that the hyperbolic bases lead to nonlinear algorithms which converge as fast as the corresponding schemes with respect to specific anisotropy adapted bases.
KW - Mathematics
KW - Anisotropic Besov spaces
KW - Dominating mixed smoothness
KW - Hyperbolic bases
KW - N-term approximation
KW - Tresholding
KW - Wavelets
UR - http://www.scopus.com/inward/record.url?scp=0036402389&partnerID=8YFLogxK
U2 - 10.1002/1522-2616(200210)244:1<131::AID-MANA131>3.0.CO;2-G
DO - 10.1002/1522-2616(200210)244:1<131::AID-MANA131>3.0.CO;2-G
M3 - Journal articles
VL - 244
SP - 131
EP - 149
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 1522-2616
IS - 1
ER -